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https://en.wikipedia.org/wiki/Psychophysical
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Psychophysical relates to the relationship between one's internal (psychic) and external (physical) worlds.
Psychophysical may refer to:
Psychophysics, the subdiscipline of psychology dealing with the relationship between physical stimuli and their subjective correlates
Psychophysiology, the branch of psychology that is concerned with the physiological bases of psychological processes including sensory processes
Psychophysical parallelism, the theory that the conscious and nervous processes vary concomitantly
See also
Psychometrics, a related field of study concerned with the theory and technique of psychological measurement
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https://en.wikipedia.org/wiki/Union%20type
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In computer science, a union is a value that may have any of several representations or formats within the same position in memory; that consists of a variable that may hold such a data structure. Some programming languages support special data types, called union types, to describe such values and variables. In other words, a union type definition will specify which of a number of permitted primitive types may be stored in its instances, e.g., "float or long integer". In contrast with a record (or structure), which could be defined to contain both a float and an integer; in a union, there is only one value at any given time.
A union can be pictured as a chunk of memory that is used to store variables of different data types. Once a new value is assigned to a field, the existing data is overwritten with the new data. The memory area storing the value has no intrinsic type (other than just bytes or words of memory), but the value can be treated as one of several abstract data types, having the type of the value that was last written to the memory area.
In type theory, a union has a sum type; this corresponds to disjoint union in mathematics.
Depending on the language and type, a union value may be used in some operations, such as assignment and comparison for equality, without knowing its specific type. Other operations may require that knowledge, either by some external information, or by the use of a tagged union.
Untagged unions
Because of the limitations of their use,
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https://en.wikipedia.org/wiki/Record%20%28computer%20science%29
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In computer science, a record (also called a structure, struct, or compound data) is a basic data structure. Records in a database or spreadsheet are usually called "rows".
A record is a collection of fields, possibly of different data types, typically in a fixed number and sequence. The fields of a record may also be called members, particularly in object-oriented programming; fields may also be called elements, though this risks confusion with the elements of a collection.
For example, a date could be stored as a record containing a numeric year field, a month field represented as a string, and a numeric day-of-month field. A personnel record might contain a name, a salary, and a rank. A Circle record might contain a center and a radius—in this instance, the center itself might be represented as a point record containing x and y coordinates.
Records are distinguished from arrays by the fact that their number of fields is determined in the definition of the record, and by the fact the records are a heterogenous data type; not all of the fields must contain the same type of data.
A record type is a data type that describes such values and variables. Most modern computer languages allow the programmer to define new record types. The definition includes specifying the data type of each field and an identifier (name or label) by which it can be accessed. In type theory, product types (with no field names) are generally preferred due to their simplicity, but proper record t
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https://en.wikipedia.org/wiki/Ljup%C4%8Do%20Jordanovski
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Ljupčo Jordanovski (, ; 13 February 1953 – 7 October 2010) was a Macedonian seismologist and politician.
Education background
Jordanovski was born in Štip. He received his BEng in Electrical Engineering from the University of Zagreb. He received his PhD from the University of Southern California in 1985.
Political activities
He was a member of the Social Democratic Union of Macedonia party. He took office as Speaker of the Assembly on 18 November 2003.
As Speaker of the Assembly, according to the Republic of Macedonia's constitution he was the successor to the president in the event of the president's inability to serve.
Acting President of Macedonia
Accordingly, when President Boris Trajkovski was killed in a plane crash on 26 February 2004, Jordanovski was sworn in as president.
He was the acting president of the Republic of Macedonia from 26 February 2004 to 12 May 2004. He left office after presidential elections in which he did not run. He continued in his role as Speaker after his time as acting president, until 2 August 2006.
Ambassador to the United States
On 6 July 2006 he was accredited as the Ambassador of the Republic of Macedonia to the United States of America, but at the end of December he was recalled by the Government of the Republic of Macedonia. He died unexpectedly in Skopje.
References
External links
– video (Macedonian)
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1953 births
2010 deaths
People from Štip
Seismologists
Speakers of the Assembly of North Macedonia
Social Democratic Uni
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https://en.wikipedia.org/wiki/Compass%20%28drawing%20tool%29
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A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.
Prior to computerization, compasses and other tools for manual drafting were often packaged as a set with interchangeable parts. By the mid-twentieth century, circle templates supplemented the use of compasses. Today those facilities are more often provided by computer-aided design programs, so the physical tools serve mainly a didactic purpose in teaching geometry, technical drawing, etc.
Construction and parts
Compasses are usually made of metal or plastic, and consist of two "legs" connected by a hinge which can be adjusted to allow changing of the radius of the circle drawn. Typically one leg has a spike at its end for anchoring, and the other leg holds a drawing tool, such as a pencil, a short length of just pencil lead or sometimes a pen.
Handle
The handle, a small knurled rod above the hinge, is usually about half an inch long. Users can grip it between their pointer finger and thumb.
Legs
There are two types of leg in a pair of compasses: the straight or the steady leg and the adjustable one. Each has a separate purpose; the steady leg serves as the basis or support for the needle point, while the adjustable leg can be altered in order to draw different sizes
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https://en.wikipedia.org/wiki/Bachem%20Holding
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Bachem Holding AG is a Swiss bio-technology company active in the fields of chemistry, biochemistry and pharmaceuticals. It specializes in the commercial production of peptides and complex organic compounds as active pharmaceutical ingredients, in the production of peptide-based biochemicals and in the development of manufacturing processes for these compounds. It was founded in 1971 and is a subsidiary of Ingro Finanz AG. The head office is in Bubendorf in the canton of Basel-Landschaft; there are production sites in Vionnaz in the canton of Valais, in the Californian cities of Vista and Torrance, and in Great Britain in St Helens near Liverpool, with a sales and distribution site in Tokyo. At the end of 2017, it had 1057 employees, revenue of CHF 261.6 million, and net income of CHF 41.8 million.
History
In 2013 the company entered an agreement with GlyTech Inc. to cooperate on the production of glycosylated proteins and peptides.
In 2015 it bought American Peptide, a bio-technology company in Sunnyvale, California.
References
External links
Biotechnology companies established in 1971
Biotechnology companies of Switzerland
Companies listed on the SIX Swiss Exchange
Companies based in Basel-Landschaft
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https://en.wikipedia.org/wiki/Inclusion%20map
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In mathematics, if is a subset of then the inclusion map (also inclusion function, insertion, or canonical injection) is the function that sends each element of to treated as an element of
A "hooked arrow" () is sometimes used in place of the function arrow above to denote an inclusion map; thus:
(However, some authors use this hooked arrow for any embedding.)
This and other analogous injective functions from substructures are sometimes called natural injections.
Given any morphism between objects and , if there is an inclusion map into the domain , then one can form the restriction of In many instances, one can also construct a canonical inclusion into the codomain known as the range of
Applications of inclusion maps
Inclusion maps tend to be homomorphisms of algebraic structures; thus, such inclusion maps are embeddings. More precisely, given a substructure closed under some operations, the inclusion map will be an embedding for tautological reasons. For example, for some binary operation to require that
is simply to say that is consistently computed in the sub-structure and the large structure. The case of a unary operation is similar; but one should also look at nullary operations, which pick out a constant element. Here the point is that closure means such constants must already be given in the substructure.
Inclusion maps are seen in algebraic topology where if is a strong deformation retract of the inclusion map yields an isomorphism between a
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https://en.wikipedia.org/wiki/Phillip%20Hagar%20Smith
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Phillip Hagar Smith (April 29, 1905 in Lexington, Massachusetts – August 29, 1987 in Berkeley Heights, New Jersey) was an electrical engineer, who became famous for his invention of the Smith chart. Smith graduated from Tufts College in 1928 with a BS degree in electrical engineering. While working for Bell Telephone Laboratories, he invented his eponymous Smith chart (which was also invented independently in 1937 by Tōsaku Mizuhashi () and in 1939 by ()).
When asked why he invented the chart, Smith explained, "From the time I could operate a slide rule, I've been interested in graphical representations of mathematical relationships." In 1969 he published the book Electronic Applications of the Smith Chart: In Waveguide, Circuit, and Component Analysis, a comprehensive work on the subject. He retired from Bell Labs in 1970. He was elected a fellow of the Institute of Radio Engineers in 1952.
Although best known for his Smith chart, he made important contributions in a variety of fields, including radar, FM, and antennas (including use of the Lüneburg lens).
The IEEE History Center conducted an interview with Smith in 1973, the edited transcript and audio clips from which are on the web.
References
1905 births
1987 deaths
Scientists at Bell Labs
Tufts University School of Engineering alumni
20th-century American engineers
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https://en.wikipedia.org/wiki/Bimodule
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In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.
Definition
If R and S are two rings, then an R-S-bimodule is an abelian group such that:
M is a left R-module and a right S-module.
For all r in R, s in S and m in M:
An R-R-bimodule is also known as an R-bimodule.
Examples
For positive integers n and m, the set Mn,m(R) of matrices of real numbers is an R-S-bimodule, where R is the ring Mn(R) of matrices, and S is the ring Mm(R) of matrices. Addition and multiplication are carried out using the usual rules of matrix addition and matrix multiplication; the heights and widths of the matrices have been chosen so that multiplication is defined. Note that Mn,m(R) itself is not a ring (unless ), because multiplying an matrix by another matrix is not defined. The crucial bimodule property, that , is the statement that multiplication of matrices is associative (which, in the case of a matrix ring, corresponds to associativity).
Any algebra A over a ring R has the natural structure of an R-bimodule, with left and right multiplication defined by and respectively, where is the canonical embedding of R into A.
If R is a ring, then R itself ca
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https://en.wikipedia.org/wiki/Patrick%20Volkerding
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Patrick Volkerding (born October 20, 1966) is the founder and maintainer of the Slackware Linux distribution. Volkerding is Slackware's "Benevolent Dictator for Life" (BDFL), and is also known informally as "The Man".
Personal life
Volkerding earned a Bachelor of Science in computer science from Minnesota State University Moorhead in 1993. Volkerding is a Deadhead, and by April 1994 had already attended 75 Grateful Dead concerts.
Volkerding is a Church of the SubGenius affiliate/member. The use of the word slack in "Slackware" is an homage to J. R. "Bob" Dobbs. About the SubGenius influence on Slackware, Volkerding has stated: "I'll admit that it was SubGenius inspired. In fact, back in the 2.0 through 3.0 days we used to print a dobbshead on each CD."
Volkerding is an avid homebrewer and beer lover. Early versions of Slackware would entreat users to send him a bottle of local beer in appreciation for his work.
Volkerding was married in 2001 to Andrea and has a daughter Briah Cecilia Volkerding (b. 2005).
Illness
In 2004, Volkerding announced via mailing list post that he was suffering from actinomycosis, a serious illness requiring multiple rounds of antibiotics and with an uncertain prognosis. This announcement caused a number of tech news outlets to wonder about the future of the Slackware project. As of 2012, both Volkerding and the Slackware project were reported to be in a healthy state again.
Slackware Linux
Michael Johnston of Morse Telecommunications paid Vol
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https://en.wikipedia.org/wiki/Order%20%28group%20theory%29
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In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element of a group, is thus the smallest positive integer such that , where denotes the identity element of the group, and denotes the product of copies of . If no such exists, the order of is infinite.
The order of a group is denoted by or , and the order of an element is denoted by or , instead of where the brackets denote the generated group.
Lagrange's theorem states that for any subgroup of a finite group , the order of the subgroup divides the order of the group; that is, is a divisor of . In particular, the order of any element is a divisor of .
Example
The symmetric group S3 has the following multiplication table.
{| class="wikitable"
|-
! •
! e || s || t || u || v || w
|-
! e
| e || s || t || u || v || w
|-
! s
| s || e || v || w || t || u
|-
! t
| t || u || e || s || w || v
|-
! u
| u || t || w || v || e || s
|-
! v
| v || w || s || e || u || t
|-
! w
| w || v || u || t || s || e
|}
This group has six elements, so . By definition, the order of the identity, , is one, since . Each of , , and squares to , so these group elements have order two: . Finally, and have order 3, since , and .
Order and structure
The o
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https://en.wikipedia.org/wiki/Cellulose%20acetate
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In biochemistry, cellulose acetate refers to any acetate ester of cellulose, usually cellulose diacetate. It was first prepared in 1865. A bioplastic, cellulose acetate is used as a film base in photography, as a component in some coatings, and as a frame material for eyeglasses; it is also used as a synthetic fiber in the manufacture of cigarette filters and playing cards. In photographic film, cellulose acetate film replaced nitrate film in the 1950s, being far less flammable and cheaper to produce.
History
In 1865, French chemist Paul Schützenberger discovered that cellulose reacts with acetic anhydride to form cellulose acetate. The German chemists Arthur Eichengrün and Theodore Becker invented the first soluble forms of cellulose acetate in 1903.
In 1904, Camille Dreyfus and his younger brother Henri performed chemical research and development on cellulose acetate in a shed in their father's garden in Basel, Switzerland, which was then a center of the dye industry. For five years, the Dreyfus brothers studied and experimented in a systematic manner in Switzerland and France. By 1910, they were producing film for the motion picture industry, and a small but constantly growing amount of acetate lacquer, called "dope", was sold to the expanding aircraft industry to coat the fabric covering wings and fuselage.
In 1913, after some twenty thousand separate experiments, they produced excellent laboratory samples of continuous filament yarn, something that had eluded the cell
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https://en.wikipedia.org/wiki/Alternating%20series
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In mathematics, an alternating series is an infinite series of the form
or
with for all . The signs of the general terms alternate between positive and negative. Like any series, an alternating series converges if and only if the associated sequence of partial sums converges.
Examples
The geometric series 1/2 − 1/4 + 1/8 − 1/16 + ⋯ sums to 1/3.
The alternating harmonic series has a finite sum but the harmonic series does not.
The Mercator series provides an analytic expression of the natural logarithm:
The functions sine and cosine used in trigonometry can be defined as alternating series in calculus even though they are introduced in elementary algebra as the ratio of sides of a right triangle. In fact,
and
When the alternating factor is removed from these series one obtains the hyperbolic functions sinh and cosh used in calculus.
For integer or positive index α the Bessel function of the first kind may be defined with the alternating series
where is the gamma function.
If is a complex number, the Dirichlet eta function is formed as an alternating series
that is used in analytic number theory.
Alternating series test
The theorem known as "Leibniz Test" or the alternating series test tells us that an alternating series will converge if the terms converge to 0 monotonically.
Proof: Suppose the sequence converges to zero and is monotone decreasing. If is odd and , we obtain the estimate via the following calculation:
Since is monotonically decreasing,
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https://en.wikipedia.org/wiki/Joshua%20Lederberg
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Joshua Lederberg, ForMemRS (May 23, 1925 – February 2, 2008) was an American molecular biologist known for his work in microbial genetics, artificial intelligence, and the United States space program. He was 33 years old when he won the 1958 Nobel Prize in Physiology or Medicine for discovering that bacteria can mate and exchange genes (bacterial conjugation). He shared the prize with Edward Tatum and George Beadle, who won for their work with genetics.
In addition to his contributions to biology, Lederberg did extensive research in artificial intelligence. This included work in the NASA experimental programs seeking life on Mars and the chemistry expert system Dendral.
Early life and education
Lederberg was born in Montclair, New Jersey, to a Jewish family, son of Esther Goldenbaum Schulman Lederberg and Rabbi Zvi Hirsch Lederberg, in 1925, and moved to Washington Heights, Manhattan as an infant. He had two younger brothers. Lederberg graduated from Stuyvesant High School in New York City at the age of 15 in 1941. After graduation, he was allowed lab space as part of the American Institute Science Laboratory, a forerunner of the Westinghouse Science Talent Search. He enrolled in Columbia University in 1941, majoring in zoology. Under the mentorship of Francis J. Ryan, he conducted biochemical and genetic studies on the bread mold Neurospora crassa. Intending to receive his MD and fulfill his military service obligations, Lederberg worked as a hospital corpsman during 1943
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https://en.wikipedia.org/wiki/Free%20algebra
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In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the polynomial ring may be regarded as a free commutative algebra.
Definition
For R a commutative ring, the free (associative, unital) algebra on n indeterminates {X1,...,Xn} is the free R-module with a basis consisting of all words over the alphabet {X1,...,Xn} (including the empty word, which is the unit of the free algebra). This R-module becomes an R-algebra by defining a multiplication as follows: the product of two basis elements is the concatenation of the corresponding words:
and the product of two arbitrary R-module elements is thus uniquely determined (because the multiplication in an R-algebra must be R-bilinear). This R-algebra is denoted R⟨X1,...,Xn⟩. This construction can easily be generalized to an arbitrary set X of indeterminates.
In short, for an arbitrary set , the free (associative, unital) R-algebra on X is
with the R-bilinear multiplication that is concatenation on words, where X* denotes the free monoid on X (i.e. words on the letters Xi), denotes the external direct sum, and Rw denotes the free R-module on 1 element, the word w.
For example, in R⟨X1,X2,X3,X4⟩, for scalars α, β, γ, δ ∈ R, a concrete example of a product of two elements is
.
The non-commutative polynomial ring may be identified with the mono
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https://en.wikipedia.org/wiki/Petrus%20Apianus
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Petrus Apianus (April 16, 1495 – April 21, 1552), also known as Peter Apian, Peter Bennewitz, and Peter Bienewitz, was a German humanist, known for his works in mathematics, astronomy and cartography. His work on "cosmography", the field that dealt with the earth and its position in the universe, was presented in his most famous publications, Astronomicum Caesareum (1540) and Cosmographicus liber (1524). His books were extremely influential in his time, with the numerous editions in multiple languages being published until 1609. The lunar crater Apianus and asteroid 19139 Apian are named in his honour.
Life and work
Apianus was born as Peter Bienewitz (or Bennewitz) in Leisnig in Saxony; his father, Martin, was a shoemaker. The family was relatively well off, belonging to the middle-class citizenry of Leisnig. Apianus was educated at the Latin school in Rochlitz. From 1516 to 1519 he studied at the University of Leipzig; during this time, he Latinized his name to Apianus (lat. apis means "bee"; "Biene" is the German word for bee).
In 1519, Apianus moved to Vienna and continued his studies at the University of Vienna, which was considered one of the leading universities in geography and mathematics at the time and where Georg Tannstetter taught. When the plague broke out in Vienna in 1521, he completed his studies with a BA and moved to Regensburg and then to Landshut. At Landshut, he produced his Cosmographicus liber (1524), a highly respected work on astronomy and naviga
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https://en.wikipedia.org/wiki/Nikolay%20Semyonov
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Nikolay Nikolayevich Semyonov (or Semënov), (; – 25 September 1986) (often referred to in English as Semenoff, Semenov, Semionov, or Semyonova) was a Soviet physicist and chemist. Semyonov was awarded the 1956 Nobel Prize in Chemistry for his work on the mechanism of chemical transformation.
Life and career
Semyonov was born in Saratov, the son of Elena Dmitrieva and Nikolai Alex Semyonov. He graduated from the department of physics of Petrograd University (1913–1917), where he was a student of Abram Fyodorovich Ioffe. In 1918, he moved to Samara, where he was enlisted into Kolchak's White Army during Russian Civil War.
Semyonov published his first research paper in 1916 and became a lecturer at the University of Tomsk in western Siberia.
After graduating from Saint Petersburg State University, he worked as an assistant and lecturer at the Tomsk and Tomsk University Institute of Technology, where he published his first research paper in 1916. He returned to western Siberia, Petrograd and took charge of the electron phenomena laboratory of the Petrograd Physico-Technical Institute in 1920. He also became the vice-director of the institute. In 1921, he married philologist Maria Boreishe-Liverovsky (student of Zhirmunsky). She died two years later. On September 15-1924, Nikolay married Maria's niece, Natalia Nikolaevna Burtseva. They had two children, one son Yurii Nikolaevich and one daughter Ludmilla Nikolaevna.
During that difficult time, Semyonov, together with Pyot
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https://en.wikipedia.org/wiki/Alexander%20Frumkin
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Alexander Naumovich Frumkin (Алекса́ндр Нау́мович Фру́мкин) (October 24, 1895 – May 27, 1976) was a Russian/Soviet electrochemist, member of the Russian Academy of Sciences since 1932, founder of the Russian Journal of Electrochemistry Elektrokhimiya and receiver of the Hero of Socialist Labor award. The Russian Academy of Sciences' A.N. Frumkin Institute of Physical Chemistry and Electrochemistry is named after him.
Biography
Early life
Frumkin was born in Kishinev, in the Bessarabia Governorate of the Russian Empire (present-day Moldova) to a Jewish family; his father was an insurance salesman. His family moved to Odessa, where he received his primary schooling; he continued his education in Strasbourg, and then at the University of Bern. Frumkin's first published articles appeared in 1914, when he was only 19; in 1915, he received his first degree, back in Odessa. Two years later, the seminal article "Electrocapillary Phenomena and Electrode Potentials" was published.
Frumkin moved to Moscow in 1922 to work at the Karpov Institute, under A.N. Bakh. In 1930, Frumkin joined the faculty of Moscow University, where in 1933 he founded—and would head until his death—the department of electrochemistry.
Frumkin was married three times, including a brief first marriage to Vera Inber.
Scientific career
During the Second World War, Frumkin led a large team of scientists and engineers involved in defense issues. This contribution did not save him from being dismissed in 1949 a
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https://en.wikipedia.org/wiki/The%20Man%20Who%20Stole%20the%20Sun
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is a 1979 Japanese thriller film, directed by Hasegawa Kazuhiko.
Plot
Makoto Kido, a high school science and chemistry teacher, has decided to build his own atomic bomb. Before stealing plutonium isotopes from Tōkai Nuclear Power Plant, he is involved in the botched hijack of one of his school's buses during a field trip. Along with a police detective, Yamashita, he is able to overcome the hijacker and is publicly hailed as a hero.
Meanwhile, Makoto is able to extract enough plutonium from his stolen isotopes to create two bombs—one genuine, the other containing only enough radioactive material to be detectable, but otherwise a fake. He plants the fake bomb in a public lavatory and phones the police and demands that Yamashita take the case. Since Makoto speaks to the police through a voice scrambler, Yamashita is unaware that Makoto is behind the whole thing.
Makoto manages to extort the government into showing baseball games without cutting away for commercials. Flush with success, he follows a suggestion by a radio personality, nicknamed "Zero", to use the real bomb to extort the government into allowing the Rolling Stones to play in Japan (despite being barred from doing so due to Keith Richards being arrested for narcotics possession). The request is soon granted and the band eventually plays in Tokyo.
As Makoto makes his way to the concert with the bomb, Yamashita follows him. Makoto pulls out a gun and forces Yamashita to a rooftop. Makoto reveals that he was
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https://en.wikipedia.org/wiki/Victor%20Babe%C8%99
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Victor Babeș (; 28 July 1854 in Vienna – 19 October 1926 in Bucharest) was a Romanian physician, bacteriologist, academician and professor. One of the founders of modern microbiology, Victor Babeș is author of one of the first treatises of bacteriology in the world – Bacteria and their role in pathological anatomy and histology of infectious diseases, written in collaboration with French scientist Victor André Cornil in 1885. In 1888, Babeș underlies the principle of passive immunity, and a few years later enunciates the principle of antibiosis. He made early and significant contributions to the study of rabies, leprosy, diphtheria, tuberculosis and other infectious diseases. He also discovered more than 50 unknown germs and foresaw new methods of staining bacteria and fungi. Victor Babeș introduced rabies vaccination and founded serotherapy in Romania.
Babeș-Bolyai University in Cluj-Napoca and the University of Medicine and Pharmacy in Timișoara bear his name.
Origin and family
Victor Babeș was the son of Vincențiu Babeș and Sophia Goldschneider. His father was a Romanian magistrate, teacher, journalist and politician from the Banat region of Hungary, founding member of the Romanian Academic Society (22 April 1866) and President of History Section of the Romanian Academy (1898–1899). One of the personalities who have distinguished themselves in the fight for the rights of Romanians in Transylvania, Vincențiu Babeș was repeatedly deputy in the Vienna Award and president o
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https://en.wikipedia.org/wiki/Brane%20cosmology
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Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory.
Brane and bulk
The central idea is that the visible, three-dimensional universe is restricted to a brane inside a higher-dimensional space, called the "bulk" (also known as "hyperspace"). If the additional dimensions are compact, then the observed universe contains the extra dimension, and then no reference to the bulk is appropriate. In the bulk model, at least some of the extra dimensions are extensive (possibly infinite), and other branes may be moving through this bulk. Interactions with the bulk, and possibly with other branes, can influence our brane and thus introduce effects not seen in more standard cosmological models.
Why gravity is weak and the cosmological constant is small
Some versions of brane cosmology, based on the large extra dimension idea, can explain the weakness of gravity relative to the other fundamental forces of nature, thus solving the hierarchy problem. In the brane picture, the electromagnetic, weak and strong nuclear force are localized on the brane, but gravity has no such constraint and propagates on the full spacetime, called the bulk. Much of the gravitational attractive power "leaks" into the bulk. As a consequence, the force of gravity should appear significantly stronger on small (subatomic or at least sub-millimetre) scales, where less gravitational force has "leaked". Various experiments are currentl
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https://en.wikipedia.org/wiki/Tris
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Tris, or tris(hydroxymethyl)aminomethane, or known during medical use as tromethamine or THAM, is an organic compound with the formula (HOCH2)3CNH2, one of the twenty Good's buffers. It is extensively used in biochemistry and molecular biology as a component of buffer solutions such as in TAE and TBE buffers, especially for solutions of nucleic acids. It contains a primary amine and thus undergoes the reactions associated with typical amines, e.g., condensations with aldehydes. Tris also complexes with metal ions in solution. In medicine, tromethamine is occasionally used as a drug, given in intensive care for its properties as a buffer for the treatment of severe metabolic acidosis in specific circumstances. Some medications are formulated as the "tromethamine salt" including Hemabate (carboprost as trometamol salt), and "ketorolac trometamol". While Good's buffers should be inert, in 2023 a strain of Pseudomonas hunanensis was found to be able to degrade TRIS buffer.
Buffering features
The conjugate acid of tris has a pKa of 8.07 at 25 °C, which implies that the buffer has an effective pH range between 7.1 and 9.1 (pKa ± 1) at room temperature.
Buffer details
In general, as temperature decreases from 25 °C to 5 °C the pH of a tris buffer will increase an average of 0.03 units per degree. As temperature rises from 25 °C to 37 °C, the pH of a tris buffer will decrease an average of 0.025 units per degree.
In general, a 10-fold increase in tris buffer concentration will lead
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https://en.wikipedia.org/wiki/Dialysis%20%28chemistry%29
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In chemistry, dialysis is the process of separating molecules in solution by the difference in their rates of diffusion through a semipermeable membrane, such as dialysis tubing.
Dialysis is a common laboratory technique that operates on the same principle as medical dialysis. In the context of life science research, the most common application of dialysis is for the removal of unwanted small molecules such as salts, reducing agents, or dyes from larger macromolecules such as proteins, DNA, or polysaccharides. Dialysis is also commonly used for buffer exchange and drug binding studies.
The concept of dialysis was introduced in 1861 by the Scottish chemist Thomas Graham. He used this technique to separate sucrose (small molecule) and gum Arabic solutes (large molecule) in aqueous solution. He called the diffusible solutes crystalloids and those that would not pass the membrane colloids.
From this concept dialysis can be defined as a spontaneous separation process of suspended colloidal particles from dissolved ions or molecules of small dimensions through a semi permeable membrane. Most common dialysis membrane are made of cellulose, modified cellulose or synthetic polymer (cellulose acetate or nitrocellulose).
Etymology
Dialysis derives from the Greek , 'through', and , 'to loosen'.
Principles
Dialysis is the process used to change the matrix of molecules in a sample by differentiating molecules by the classification of size. It relies on diffusion, which is the random,
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https://en.wikipedia.org/wiki/Assay
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An assay is an investigative (analytic) procedure in laboratory medicine, mining, pharmacology, environmental biology and molecular biology for qualitatively assessing or quantitatively measuring the presence, amount, or functional activity of a target entity. The measured entity is often called the analyte, the measurand, or the target of the assay. The analyte can be a drug, biochemical substance, chemical element or compound, or cell in an organism or organic sample. An assay usually aims to measure an analyte's intensive property and express it in the relevant measurement unit (e.g. molarity, density, functional activity in enzyme international units, degree of effect in comparison to a standard, etc.).
If the assay involves exogenous reactants (the reagents), then their quantities are kept fixed (or in excess) so that the quantity and quality of the target are the only limiting factors. The difference in the assay outcome is used to deduce the unknown quality or quantity of the target in question. Some assays (e.g., biochemical assays) may be similar to chemical analysis and titration. However, assays typically involve biological material or phenomena that are intrinsically more complex in composition or behavior, or both. Thus, reading of an assay may be noisy and involve greater difficulties in interpretation than an accurate chemical titration. On the other hand, older generation qualitative assays, especially bioassays, may be much more gross and less quantitative (
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https://en.wikipedia.org/wiki/Nuclease
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In biochemistry, a nuclease (also archaically known as nucleodepolymerase or polynucleotidase) is an enzyme capable of cleaving the phosphodiester bonds between nucleotides of nucleic acids. Nucleases variously effect single and double stranded breaks in their target molecules. In living organisms, they are essential machinery for many aspects of DNA repair. Defects in certain nucleases can cause genetic instability or immunodeficiency. Nucleases are also extensively used in molecular cloning.
There are two primary classifications based on the locus of activity. Exonucleases digest nucleic acids from the ends. Endonucleases act on regions in the middle of target molecules. They are further subcategorized as deoxyribonucleases and ribonucleases. The former acts on DNA, the latter on RNA.
History
In the late 1960s, scientists Stuart Linn and Werner Arber isolated examples of the two types of enzymes responsible for phage growth restriction in Escherichia coli (E. coli) bacteria. One of these enzymes added a methyl group to the DNA, generating methylated DNA, while the other cleaved unmethylated DNA at a wide variety of locations along the length of the molecule. The first type of enzyme was called a "methylase" and the other a "restriction nuclease". These enzymatic tools were important to scientists who were gathering the tools needed to "cut and paste" DNA molecules. What was then needed was a tool that would cut DNA at specific sites, rather than at random sites along the
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https://en.wikipedia.org/wiki/Michael%20Duff%20%28physicist%29
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Michael James Duff FRS, FRSA is a British theoretical physicist and pioneering theorist of supergravity who is the Principal of the Faculty of Physical Sciences and Abdus Salam Chair of Theoretical Physics at Imperial College London.
Education
Duff completed his Bachelor of Science in Physics Queen Mary College, London in 1969. He then went on to his Doctor of Philosophy in theoretical physics in 1972 at Imperial College London supervised by the Nobel Laureate Abdus Salam. He did postdoctoral fellowships at the International Centre for Theoretical Physics, University of Oxford, King's College London, Queen Mary College London and Brandeis University.
Academic career
After his postdoctoral fellowships, he returned to Imperial College in 1979 on a Science Research Council Advanced Fellowship and joined the faculty there in 1980. He took leave of absence to visit the Theory Division in CERN, first in 1982 and then again as a Staff Member from 1984 to 1987 when he became Senior Physicist. He has held Visiting Professorships and Fellowships at the University of Texas, Austin; the University of California, Santa Barbara, the University of Kyoto and the Isaac Newton Institute, University of Cambridge. He took up his professorship at Texas A&M University in 1988 and was appointed Distinguished Professor in 1992. In 1999 he moved to the University of Michigan, where he was Oskar Klein Professor of Physics. In 2001, he was elected first Director of the Michigan Center for Theoretica
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https://en.wikipedia.org/wiki/Wobble
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Wobble or wobbles may refer to:
"Wobble" (song), a single by V.I.C.
"Wobble", a song by Flo Rida from his 2015 EP My House
Wobbles (equine disorder), a disorder of the nervous system in dogs and horses
Wobble base pair, a type of base pairing in genetics
Chandler wobble, short-term periodic change in Earth's axial tilt
Jah Wobble (born 1958), British musician
Milankovitch wobble, long-term change in the Earth's axial tilt, axial precession and orbital eccentricity
Speed wobble, a quick oscillation of primarily just the steerable wheel(s) of a vehicle
A metasyntactic variable, commonly used alongside wibble, wubble, and flob
See also
Wobbler (disambiguation)
Weeble, several lines of children's roly-poly toys
Doppler spectroscopy in astronomy, also known as the wobble method
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https://en.wikipedia.org/wiki/Rationalization
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Rationalization may refer to:
Rationalization (economics), an attempt to change an ad hoc workflow into one based on published rules; also, jargon for a reduction in staff
Rationalisation (mathematics), the process of removing a square root or imaginary number from the denominator of a fraction
Rationalization (psychology), a psychological defense mechanism in which perceived controversial behaviors are logically justified also known as "making excuses"
Post-purchase rationalization, a tendency to retroactively ascribe positive attributes to an option one has selected
Rationalization (sociology), the replacement of traditions, values, and emotions as motives for behavior in society with rational motives
Rationalization, appropriate placement of a factor such as was done with for Heaviside–Lorentz units
See also
Rational (disambiguation)
Rationale (disambiguation)
Rationalism (disambiguation)
Rationality
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https://en.wikipedia.org/wiki/CSNET
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The Computer Science Network (CSNET) was a computer network that began operation in 1981 in the United States. Its purpose was to extend networking benefits, for computer science departments at academic and research institutions that could not be directly connected to ARPANET, due to funding or authorization limitations. It played a significant role in spreading awareness of, and access to, national networking and was a major milestone on the path to development of the global Internet. CSNET was funded by the National Science Foundation for an initial three-year period from 1981 to 1984.
History
Lawrence Landweber at the University of Wisconsin–Madison prepared the original CSNET proposal, on behalf of a consortium of universities (Georgia Tech, University of Minnesota, University of New Mexico, University of Oklahoma, Purdue University, University of California, Berkeley, University of Utah, University of Virginia, University of Washington, University of Wisconsin, and Yale University). The US National Science Foundation (NSF) requested a review from David J. Farber at the University of Delaware. Farber assigned the task to his graduate student Dave Crocker who was already active in the development of electronic mail. The project was deemed interesting but in need of significant refinement. The proposal eventually gained the support of Vinton Cerf and DARPA. In 1980, the NSF awarded $5 million to launch the network. It was an unusually large project for the NSF at the ti
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https://en.wikipedia.org/wiki/Cohen%E2%80%93Macaulay%20ring
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In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central role in commutative algebra: they form a very broad class, and yet they are well understood in many ways.
They are named for , who proved the unmixedness theorem for polynomial rings, and for , who proved the unmixedness theorem for formal power series rings. All Cohen–Macaulay rings have the unmixedness property.
For Noetherian local rings, there is the following chain of inclusions.
Definition
For a commutative Noetherian local ring R, a finite (i.e. finitely generated) R-module is a Cohen-Macaulay module if (in general we have: , see Auslander–Buchsbaum formula for the relation between depth and dim of a certain kind of modules). On the other hand, is a module on itself, so we call a Cohen-Macaulay ring if it is a Cohen-Macaulay module as an -module. A maximal Cohen-Macaulay module is a Cohen-Macaulay module M such that .
The above definition was for a Noetherian local rings. But we can expand the definition for a more general Noetherian ring: If is a commutative Noetherian ring, then an R-module M is called Cohen–Macaulay module if is a Cohen-Macaulay module for all maximal ideals . (This is a kind of circular definition unless we def
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https://en.wikipedia.org/wiki/Riemann%E2%80%93Hurwitz%20formula
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In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It is a prototype result for many others, and is often applied in the theory of Riemann surfaces (which is its origin) and algebraic curves.
Statement
For a compact, connected, orientable surface , the Euler characteristic is
,
where g is the genus (the number of handles), since the Betti numbers are . In the case of an (unramified) covering map of surfaces
that is surjective and of degree , we have the formula
That is because each simplex of should be covered by exactly in , at least if we use a fine enough triangulation of , as we are entitled to do since the Euler characteristic is a topological invariant. What the Riemann–Hurwitz formula does is to add in a correction to allow for ramification (sheets coming together).
Now assume that and are Riemann surfaces, and that the map is complex analytic. The map is said to be ramified at a point P in S′ if there exist analytic coordinates near P and π(P) such that π takes the form π(z) = zn, and n > 1. An equivalent way of thinking about this is that there exists a small neighborhood U of P such that π(P) has exactly one preimage in U, but the image of any other point in U has exactly n preimages in U. The number n is called the ram
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https://en.wikipedia.org/wiki/Cannonball%20%28disambiguation%29
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A cannonball is round shot ammunition for a cannon.
Cannonball or cannon ball may also refer to:
Biology
Couroupita guianensis, an evergreen tree commonly called the cannonball tree
Sphaerobolus, a genus commonly known as the cannonball fungi
Cannonball jellyfish, a species of jellyfish
Film and television
Cannonball (film), a 1976 film inspired by "Cannon Ball" Baker
Cannonball (TV series), a TV show about two truck drivers, produced in Canada in 1958–59 and syndicated in the U.S. in 1959–60
Cannonball (Australian game show)
Cannonball (British game show)
Cannonball (American game show)
"Cannonball", a 2003 episode of Lilo & Stitch: The Series
Hooterville Cannonball, a fictional train in the television series Petticoat Junction
Music
Albums
Cannonball (album), by Pat Green, 2006
Cannonball!!!, by Bleubird, 2012
Songs
"Cannonball" (The Breeders song), 1993
"Cannonball" (Damien Rice song), 2002; covered by Little Mix, 2011
"Cannonball" (Duane Eddy song), 1958
"Cannonball" (Lea Michele song), 2013
"Cannonball" (Showtek and Justin Prime song), 2013
"Cannonball" (Skylar Grey song), 2015
"Cannonball" (Supertramp song), 1985
"Cannonball" (Tom Dice song), 2017
"Cannonball", by Alestorm from Seventh Rum of a Seventh Rum, 2022
"Cannonball", by Brandi Carlile from The Story, 2007
"Cannonball", by Dog Eat Dog, 2005
"Cannonball", by Five Iron Frenzy from The End Is Near, 2004
"Cannonball", by Grouplove from Big Mess, 2016
"Cannonball", by Gudda Gudda, feat
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https://en.wikipedia.org/wiki/Centered%20hexagonal%20number
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In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal numbers:
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! 1 !! !! 7 !! !! 19 !! !! 37
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Centered hexagonal numbers should not be confused with cornered hexagonal numbers, which are figurate numbers in which the associated hexagons share a vertex.
The sequence of hexagonal numbers starts out as follows :
1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919.
Formula
The th centered hexagonal number is given by the formula
Expressing the formula as
shows that the centered hexagonal number for is 1 more than 6 times the th triangular number.
In the opposite direction, the index corresponding to the centered hexagonal number can be calculated using the formula
This can be used as a test for whether a number is centered hexagonal: it will be if and only if the above expression is an integer.
Recurrence and generating function
The centered hexagonal numbers satisfy the recurrence relation
From this we can calcul
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https://en.wikipedia.org/wiki/MD5CRK
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In cryptography, MD5CRK was a volunteer computing effort (similar to distributed.net) launched by Jean-Luc Cooke and his company, CertainKey Cryptosystems, to demonstrate that the MD5 message digest algorithm is insecure by finding a collision two messages that produce the same MD5 hash. The project went live on March 1, 2004. The project ended on August 24, 2004 after researchers independently demonstrated a technique for generating collisions in MD5 using analytical methods by Xiaoyun Wang, Feng, Xuejia Lai, and Yu. CertainKey awarded a 10,000 Canadian Dollar prize to Wang, Feng, Lai and Yu for their discovery.
A technique called Floyd's cycle-finding algorithm was used to try to find a collision for MD5. The algorithm can be described by analogy with a random walk. Using the principle that any function with a finite number of possible outputs placed in a feedback loop will cycle, one can use a relatively small amount of memory to store outputs with particular structures and use them as "markers" to better detect when a marker has been "passed" before. These markers are called distinguished points, the point where two inputs produce the same output is called a collision point. MD5CRK considered any point whose first 32 bits were zeroes to be a distinguished point.
Complexity
The expected time to find a collision is not equal to where is the number of bits in the digest output. It is in fact , where is the number of function outputs collected.
For this project, the
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https://en.wikipedia.org/wiki/2-satisfiability
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In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. It is a special case of the general Boolean satisfiability problem, which can involve constraints on more than two variables, and of constraint satisfaction problems, which can allow more than two choices for the value of each variable. But in contrast to those more general problems, which are NP-complete, 2-satisfiability can be solved in polynomial time.
Instances of the 2-satisfiability problem are typically expressed as Boolean formulas of a special type, called conjunctive normal form (2-CNF) or Krom formulas. Alternatively, they may be expressed as a special type of directed graph, the implication graph, which expresses the variables of an instance and their negations as vertices in a graph, and constraints on pairs of variables as directed edges. Both of these kinds of inputs may be solved in linear time, either by a method based on backtracking or by using the strongly connected components of the implication graph. Resolution, a method for combining pairs of constraints to make additional valid constraints, also leads to a polynomial time solution. The 2-satisfiability problems provide one of two major subclasses of the conjunctive normal form formulas that can be solved in polynomial time; the other of the two subclasses is Horn-satisfiability.
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https://en.wikipedia.org/wiki/Terminator%20%28genetics%29
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In genetics, a transcription terminator is a section of nucleic acid sequence that marks the end of a gene or operon in genomic DNA during transcription. This sequence mediates transcriptional termination by providing signals in the newly synthesized transcript RNA that trigger processes which release the transcript RNA from the transcriptional complex. These processes include the direct interaction of the mRNA secondary structure with the complex and/or the indirect activities of recruited termination factors. Release of the transcriptional complex frees RNA polymerase and related transcriptional machinery to begin transcription of new mRNAs.
In prokaryotes
Two classes of transcription terminators, Rho-dependent and Rho-independent, have been identified throughout prokaryotic genomes. These widely distributed sequences are responsible for triggering the end of transcription upon normal completion of gene or operon transcription, mediating early termination of transcripts as a means of regulation such as that observed in transcriptional attenuation, and to ensure the termination of runaway transcriptional complexes that manage to escape earlier terminators by chance, which prevents unnecessary energy expenditure for the cell.
Rho-dependent terminators
Rho-dependent transcription terminators require a large protein called a Rho factor which exhibits RNA helicase activity to disrupt the mRNA-DNA-RNA polymerase transcriptional complex. Rho-dependent terminators are found in
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https://en.wikipedia.org/wiki/STS-40
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STS-40, the eleventh launch of Space Shuttle Columbia, was a nine-day mission in June 1991. It carried the Spacelab module for Spacelab Life Sciences 1 (SLS-1), the fifth Spacelab mission and the first dedicated solely to biology. STS-40 was the first spaceflight that included three women crew members.
Crew
Backup crew
Crew seating arrangements
Mission highlights
The launch was originally set for May 22, 1991. The mission was postponed less than 48 hours before launch when it became known that a leaking liquid hydrogen transducer in the orbiter's main propulsion system, which was removed and replaced during leak testing in 1990, had failed an analysis by a vendor. Engineers feared that one or more of the nine liquid hydrogen and liquid oxygen transducers protruding into fuel and oxidizer lines could break off and be ingested by the engine turbopumps, causing engine failure.
In addition, one of the orbiter's five general purpose computers failed completely, along with one of the multiplexer demultiplexers that controlled the orbiter's hydraulics ordinance and Orbital Maneuvering System / Reaction Control System functions in the aft compartment.
A new general purpose computer and multiplexer demultiplexer were installed and tested. One liquid hydrogen and two liquid oxygen transducers were replaced upstream in the propellant flow system near the disconnect area, which is protected by internal screen. Three liquid oxygen transducers were replaced in the engine manifold
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https://en.wikipedia.org/wiki/Closed%20graph%20theorem
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In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs.
Each gives conditions when functions with closed graphs are necessarily continuous.
Graphs and maps with closed graphs
If is a map between topological spaces then the graph of is the set or equivalently,
It is said that the graph of is closed if is a closed subset of (with the product topology).
Any continuous function into a Hausdorff space has a closed graph.
Any linear map, between two topological vector spaces whose topologies are (Cauchy) complete with respect to translation invariant metrics, and if in addition (1a) is sequentially continuous in the sense of the product topology, then the map is continuous and its graph, , is necessarily closed. Conversely, if is such a linear map with, in place of (1a), the graph of is (1b) known to be closed in the Cartesian product space , then is continuous and therefore necessarily sequentially continuous.
Examples of continuous maps that do not have a closed graph
If is any space then the identity map is continuous but its graph, which is the diagonal , is closed in if and only if is Hausdorff. In particular, if is not Hausdorff then is continuous but does have a closed graph.
Let denote the real numbers with the usual Euclidean topology and let denote with the indiscrete topology (where note that is Hausdorff and that every function valued in is con
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https://en.wikipedia.org/wiki/Donald%20J.%20Cram
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Donald James Cram (April 22, 1919 – June 17, 2001) was an American chemist who shared the 1987 Nobel Prize in Chemistry with Jean-Marie Lehn and Charles J. Pedersen "for their development and use of molecules with structure-specific interactions of high selectivity." They were the founders of the field of host–guest chemistry.
Early life and education
Cram was born and raised in Chester, Vermont, to a Scottish immigrant father, and a German immigrant mother. His father died before Cram turned four, leaving him the only male in a family of five. He grew up on Aid to Dependent Children, and learned to work at an early age, doing jobs such as picking fruit, tossing newspapers, and painting houses, while bartering for piano lessons. By the time he turned eighteen, he had worked at least eighteen different jobs.
Cram attended the Winwood High School in Long Island, N.Y.
From 1938 to 1941, he attended Rollins College in Winter Park, Florida on a national honorary scholarship, where he worked as an assistant in the chemistry department, and was active in theater, chapel choir, Lambda Chi Alpha, Phi Society, and Zeta Alpha Epsilon. It was at Rollins that he became known for building his own chemistry equipment. In 1941, he graduated from Rollins College with a BS in chemistry.
In 1942, he graduated from the University of Nebraska–Lincoln with a MS in organic chemistry, with Norman O. Cromwell serving as his thesis adviser. His subject was "Amino ketones, mechanism studies of the r
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https://en.wikipedia.org/wiki/Program%20synthesis
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In computer science, program synthesis is the task to construct a program that provably satisfies a given high-level formal specification. In contrast to program verification, the program is to be constructed rather than given; however, both fields make use of formal proof techniques, and both comprise approaches of different degrees of automatization. In contrast to automatic programming techniques, specifications in program synthesis are usually non-algorithmic statements in an appropriate logical calculus.
Origin
During the Summer Institute of Symbolic Logic at Cornell University in 1957, Alonzo Church defined the problem to synthesize a circuit from mathematical requirements. Even though the work only refers to circuits and not programs, the work is considered to be one of the earliest descriptions of program synthesis and some researchers refer to program synthesis as "Church's Problem". In the 1960s, a similar idea for an "automatic programmer" was explored by researchers in artificial intelligence.
Since then, various research communities considered the problem of program synthesis. Notable works include the 1969 automata-theoretic approach by Büchi and Landweber, and the works by Manna and Waldinger (c. 1980). The development of modern high-level programming languages can also be understood as a form of program synthesis.
21st century developments
The early 21st century has seen a surge of practical interest in the idea of program synthesis in the formal verific
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https://en.wikipedia.org/wiki/Effective%20nuclear%20charge
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In atomic physics, the effective nuclear charge is the actual amount of positive (nuclear) charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevent higher energy electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner layer. The effective nuclear charge experienced by an electron is also called the core charge. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom. Most of the physical and chemical properties of the elements can be explained on the basis of electronic configuration. Consider the behavior of ionization energies in the periodic table. It is known that the magnitude of ionization potential depends upon the following factors:
Size of atom;
The nuclear charge;
The screening effect of the inner shells, and
The extent to which the outermost electron penetrates into the charge cloud set up by the inner lying electron.
In the periodic table, effective nuclear charge decreases down a group and increases left to right across a period.
Description
The effective atomic number Zeff, (sometimes referred to as the effective nuclear charge) of an atom is the number of protons that an electron in the element effectively 'sees' due to screening by inner-shell electrons. It is a measure of the electrostatic interaction between the negatively charged electrons and positively charged
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https://en.wikipedia.org/wiki/Aldol
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In organic chemistry, an aldol describes a structural motif consisting of a 3-hydroxy ketone, , or 3-hydroxyaldehyde, . Both are composed of a hydroxy group () and either a ketone () or an aldehyde (, which is merely a ketone with a hydrogen substituent). An aldol consisting of a 3-hydroxy ketone is called a β-hydroxy ketone, and an aldol consisting of a 3-hydroxy aldehyde is called a β-hydroxy aldehyde. The term "aldol" may refer to 3-hydroxybutanal.
Synthesis and reactions
Aldols are usually the product of aldol addition, i.e. the condensation of two aldehydes. Stereoselective syntheses of aldols is an active area of asymmetric synthesis.
The chemistry of aldols is dominated by one reaction, dehydration:
RC(O)CH2CH(OH)R' → RC(O)CH=CHR' + H2O
Applications
When two molecules of aldehydes react to form an aldol (β-hydroxy aldehyde), the aldol usually produces secondary compounds since it is unstable. Secondary compounds can be diols, unsaturated aldehydes, or alcohols. The aldol 3-hydroxybutanal is a precursor to quinaldine, a precursor to the dye quinoline Yellow SS.
Aldols are also used as intermediates in the synthesis of natural products and drugs. The synthesis of Oseltamivir, an antiviral medicine used to treat the flu, involves the aldol reaction.
The structural motif of aldols is often found in polyketide natural products, which can be used to manufacture antibiotics.
Hydroxypivaldehyde is a rare example of a relatively robust aldol.
See also
Mukaiyama ald
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https://en.wikipedia.org/wiki/Aldol%20condensation
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An aldol condensation is a condensation reaction in organic chemistry in which two carbonyl moieties (of aldehydes or ketones) react to form a β-hydroxyaldehyde or β-hydroxyketone (an aldol reaction), and this is then followed by dehydration to give a conjugated enone.
The overall reaction equation is as follows (where the Rs can be H)
Aldol condensations are important in organic synthesis and biochemistry as ways to form carbon–carbon bonds.
In its usual form, it involves the nucleophilic addition of a ketone enolate to an aldehyde to form a β-hydroxy ketone, or aldol (aldehyde + alcohol), a structural unit found in many naturally occurring molecules and pharmaceuticals.
The term aldol condensation is also commonly used, especially in biochemistry, to refer to just the first (addition) stage of the process—the aldol reaction itself—as catalyzed by aldolases. However, the first step is formally an addition reaction rather than a condensation reaction because it does not involve the loss of a small molecule.
Mechanism
The first part of this reaction is an Aldol reaction, the second part a dehydration—an elimination reaction (Involves removal of a water molecule or an alcohol molecule). Dehydration may be accompanied by decarboxylation when an activated carboxyl group is present. The aldol addition product can be dehydrated via two mechanisms; a strong base like potassium t-butoxide, potassium hydroxide or sodium hydride deprotonates the product to an enolate, which elimi
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https://en.wikipedia.org/wiki/Steiner%20tree%20problem
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In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Steiner tree problems may be formulated in a number of settings, they all require an optimal interconnect for a given set of objects and a predefined objective function. One well-known variant, which is often used synonymously with the term Steiner tree problem, is the Steiner tree problem in graphs. Given an undirected graph with non-negative edge weights and a subset of vertices, usually referred to as terminals, the Steiner tree problem in graphs requires a tree of minimum weight that contains all terminals (but may include additional vertices) and minimizes the total weight of its edges. Further well-known variants are the Euclidean Steiner tree problem and the rectilinear minimum Steiner tree problem.
The Steiner tree problem in graphs can be seen as a generalization of two other famous combinatorial optimization problems: the (non-negative) shortest path problem and the minimum spanning tree problem. If a Steiner tree problem in graphs contains exactly two terminals, it reduces to finding the shortest path. If, on the other hand, all vertices are terminals, the Steiner tree problem in graphs is equivalent to the minimum spanning tree. However, while both the non-negative shortest path and the minimum spanning tree problem are solvable in polynomial time, no such solution is
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https://en.wikipedia.org/wiki/Identification%20key
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In biology, an identification key, taxonomic key, or biological key is a printed or computer-aided device that aids the identification of biological entities, such as plants, animals, fossils, microorganisms, and pollen grains. Identification keys are also used in many other scientific and technical fields to identify various kinds of entities, such as diseases, soil types, minerals, or archaeological and anthropological artifacts.
Traditionally identification keys have most commonly taken the form of single-access keys. These work by offering a fixed sequence of identification steps, each with multiple alternatives, the choice of which determines the next step. If each step has only two alternatives, the key is said to be dichotomous, else it is polytomous. Modern multi-access or interactive keys allow the user to freely choose the identification steps and their order.
At each step, the user must answer a question about one or more features (characters) of the entity to be identified. For example, a step in a botanical key may ask about the color of flowers, or the disposition of the leaves along the stems. A key for insect identification may ask about the number of bristles on the rear leg.
Principles of good key design
Identification errors may have serious consequences in both pure and applied disciplines, including ecology, medical diagnosis, pest control, forensics, etc. Therefore, identification keys must be constructed with great care in order to minimize the
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https://en.wikipedia.org/wiki/Initial%20value%20problem
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In multivariable calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem. In that context, the differential initial value is an equation which specifies how the system evolves with time given the initial conditions of the problem.
Definition
An initial value problem is a differential equation
with where is an open set of ,
together with a point in the domain of
called the initial condition.
A solution to an initial value problem is a function that is a solution to the differential equation and satisfies
In higher dimensions, the differential equation is replaced with a family of equations , and is viewed as the vector , most commonly associated with the position in space. More generally, the unknown function can take values on infinite dimensional spaces, such as Banach spaces or spaces of distributions.
Initial value problems are extended to higher orders by treating the derivatives in the same way as an independent function, e.g. .
Existence and uniqueness of solutions
The Picard–Lindelöf theorem guarantees a unique solution on some interval containing t0 if f is continuous on a region containing t0 and y0 and satisfies the Lipschitz condition on the variable y.
The proof of this theorem proceeds by reformulating the pr
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https://en.wikipedia.org/wiki/David%20J.%20Griffiths
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David Jeffrey Griffiths (born December 5, 1942) is an American physicist and educator. He was on the faculty of Reed College from 1978 through 2009, becoming the Howard Vollum Professor of Science before his retirement. He wrote three highly regarded textbooks for undergraduate physics students.
Early life and education
Griffiths was born in Arlington, Virginia, the son of Winifred Mary (née Jeffrey) and Gordon Griffiths. Both his parents were faculty members at the University of Washington, his father in the history department and his mother in the zoology department.
Griffiths is a graduate of The Putney School and was trained at Harvard University (B.A., 1964; M.A., 1966; Ph.D., 1970). His doctoral work, Covariant Approach to Massless Field Theory in the Radiation Gauge on theoretical particle physics, was supervised by Sidney Coleman.
Career
Griffiths is principally known as the author of three highly regarded textbooks for undergraduate physics students: Introduction to Elementary Particles (published in 1987, second edition published 2008), Introduction to Quantum Mechanics (published in 1995, third edition published 2018), and Introduction to Electrodynamics (published in 1981, fourth edition published in 2012).
Awards, honors
Griffiths was the recipient of the 1997 Robert A. Millikan award reserved for "those who have made outstanding scholarly contributions to physics education".
In 2009 Griffiths was named a Fellow of the American Physical Society, cited
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https://en.wikipedia.org/wiki/115%20%28number%29
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115 (one hundred [and] fifteen) is the natural number following 114 and preceding 116.
In mathematics
115 has a square sum of divisors:
There are 115 different rooted trees with exactly eight nodes, 115 inequivalent ways of placing six rooks on a 6 × 6 chess board in such a way that no two of the rooks attack each other, and 115 solutions to the stamp folding problem for a strip of seven stamps.
115 is also a heptagonal pyramidal number. The 115th Woodall number,
is a prime number.
115 is the sum of the first five heptagonal numbers.
See also
115 (disambiguation)
References
Integers
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https://en.wikipedia.org/wiki/116%20%28number%29
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116 (one hundred [and] sixteen) is the natural number following 115 and preceding 117.
In mathematics
116 is a noncototient, meaning that there is no solution to the equation , where stands for Euler's totient function.
116! + 1 is a factorial prime.
There are 116 ternary Lyndon words of length six, and 116 irreducible polynomials of degree six over a three-element field, which form the basis of a free Lie algebra of dimension 116.
There are 116 different ways of partitioning the numbers from 1 through 5 into subsets in such a way that, for every k, the union of the first k subsets is a consecutive sequence of integers.
There are 116 different 6×6 Costas arrays.
See also
116 (disambiguation)
References
Integers
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https://en.wikipedia.org/wiki/117%20%28number%29
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117 (one hundred [and] seventeen) is the natural number following 116 and preceding 118.
In mathematics
117 is the smallest possible length of the longest edge of an integer Heronian tetrahedron (a tetrahedron whose edge lengths, face areas and volume are all integers). Its other edge lengths are 51, 52, 53, 80 and 84.
117 is a pentagonal number.
In other fields
117 can be a substitute for the number 17, which is considered unlucky in Italy. When Renault exported the R17 to Italy, it was renamed R117.
Chinese dragons are usually depicted as having 117 scales, subdivided into 81 associated with yang and 36 associated with yin.
In the Danish language the number 117 () is often used as a hyperbolic term to represent an arbitrary but large number.
See also
117 (disambiguation)
References
Integers
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https://en.wikipedia.org/wiki/118%20%28number%29
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118 (one hundred [and] eighteen) is the natural number following 117 and preceding 119.
In mathematics
There is no answer to the equation φ(x) = 118, making 118 a nontotient.
Four expressions for 118 as the sum of three positive integers have the same product:
14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118 and
14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800.
118 is the smallest number that can be expressed as four sums with the same product in this way.
Because of its expression as , it is a Leyland number of the second kind.
118!! - 1 is a prime number, where !! denotes the double factorial (the product of even integers up to 118).
In other fields
There are 118 known elements on the Periodic Table, the 118th element being oganesson.
See also
118 (disambiguation)
References
Integers
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https://en.wikipedia.org/wiki/Mantis%20%28disambiguation%29
|
Mantis is the common name of any insect in the order Mantodea, also commonly known as praying mantises.
Mantis may also refer to:
Science and technology
Biology
Mantis (genus), a genus of mantises
Mantis shrimp, also known as stomatopods, predatory crustaceans
Mantispidae or mantis-flies, small predatory insects whose front legs are similar to those of a praying mantis
Computing
MANTIS, a programming language or an application generator marketed by Cincom
Mantis Bug Tracker, a bug tracking system
Spacecraft
MANTIS (spacecraft), "Main-belt Asteroid and NEO Tour with Imaging and Spectroscopy", a proposed NASA spacecraft that would flyby multiple asteroids
MANTIS (space telescope), "Monitoring Activity from Nearby Stars with UV Imaging and Spectroscopy", a planned NASA space telescope
Arts and entertainment
Mantis (album), a 2009 studio album by progressive rock/jam band Umphrey's McGee
The Mantis, a 2023 novel in the Hitman franchise by Kōtarō Isaka
Comics
Mantis (DC Comics), a supervillain in Jack Kirby's Fourth World
Mantis (Marvel Comics), a member of The Avengers
Mantis (Marvel Cinematic Universe), the Marvel Cinematic Universe version of the character
Games
Psycho Mantis, a boss in the videogame Metal Gear Solid
Mantis, an alien insect-like race in the real-time strategy computer game Conquest: Frontier Wars
Mantis, an alien race in the MMORPG Pirate Galaxy
XF5700 Mantis, a space sim by MicroPlay in 1992
The Mantis, an alien insect-like race in the r
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https://en.wikipedia.org/wiki/Path%20length
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Path length can refer to:
Physics
Distance, the total distance an object travels dependent on its path through space
Optical path length, the product of the distance light travels and the refractive index of the medium it travels through
Mean free path, the average distance that a particle travels before scattering
Radiation length, a characteristic length for the decay of radiation in a medium
Networks and computing
Average path length, the average number of steps along the shortest paths for all possible pairs of network nodes
Hop count, the number of intermediate network devices through which data must pass between source and destination in a computer network
Instruction path length, the number of machine code instructions required to execute a section of a computer program
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https://en.wikipedia.org/wiki/Growth%20rate
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Growth rate may refer to:
By rate
Asymptotic analysis, a branch of mathematics concerned with the analysis of growth rates
Linear growth
Exponential growth, a growth rate classification
Any of a variety of growth rates classified by such things as the Landau notation
By type of growing medium
Economic growth, the increase in value of the goods and services produced by an economy
Compound annual growth rate or CAGR, a measure of financial growth
Population growth rate, change in population over time
Growth rate (group theory), a property of a group in group theory
In biology
The rate of growth in any biological system, see Growth § Biology.
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https://en.wikipedia.org/wiki/Lindbladian
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In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, Andrzej Kossakowski, George Sudarshan and Göran Lindblad), master equation in Lindblad form, quantum Liouvillian, or Lindbladian is one of the general forms of Markovian master equations describing open quantum systems. It generalizes the Schrödinger equation to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics is no longer unitary, but still satisfies the property of being trace-preserving and completely positive for any initial condition.
The Schrödinger equation or, actually, the von Neumann equation, is a special case of the GKSL equation, which has led to some speculation that quantum mechanics may be productively extended and expanded through further application and analysis of the Lindblad equation. The Schrödinger equation deals with state vectors, which can only describe pure quantum states and are thus less general than density matrices, which can describe mixed states as well.
Motivation
In the canonical formulation of quantum mechanics, a system's time evolution is governed by unitary dynamics. This implies that there is no decay and phase coherence is maintained throughout the process, and is a consequence of the fact that all participating degrees of freedom are considered. However, any real physical system is not absolutely isolated, and will interact with its environment. This interaction w
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https://en.wikipedia.org/wiki/Polymorphism%20%28biology%29
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In biology, polymorphism is the occurrence of two or more clearly different morphs or forms, also referred to as alternative phenotypes, in the population of a species. To be classified as such, morphs must occupy the same habitat at the same time and belong to a panmictic population (one with random mating).
Put simply, polymorphism is when there are two or more possibilities of a trait on a gene. For example, there is more than one possible trait in terms of a jaguar's skin colouring; they can be light morph or dark morph. Due to having more than one possible variation for this gene, it is termed 'polymorphism'. However, if the jaguar has only one possible trait for that gene, it would be termed "monomorphic". For example, if there was only one possible skin colour that a jaguar could have, it would be termed monomorphic.
The term polyphenism can be used to clarify that the different forms arise from the same genotype. Genetic polymorphism is a term used somewhat differently by geneticists and molecular biologists to describe certain mutations in the genotype, such as single nucleotide polymorphisms that may not always correspond to a phenotype, but always corresponds to a branch in the genetic tree. See below.
Polymorphism is common in nature; it is related to biodiversity, genetic variation, and adaptation. Polymorphism usually functions to retain a variety of forms in a population living in a varied environment. The most common example is sexual dimorphism, which occu
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https://en.wikipedia.org/wiki/RSA%20Factoring%20Challenge
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The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them. The smallest of them, a 100-decimal digit number called RSA-100 was factored by April 1, 1991. Many of the bigger numbers have still not been factored and are expected to remain unfactored for quite some time, however advances in quantum computers make this prediction uncertain due to Shor's algorithm.
In 2001, RSA Laboratories expanded the factoring challenge and offered prizes ranging from $10,000 to $200,000 for factoring numbers from 576 bits up to 2048 bits.
The RSA Factoring Challenges ended in 2007. RSA Laboratories stated: "Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active." When the challenge ended in 2007, only RSA-576 and RSA-640 had been factored from the 2001 challenge numbers.
The factoring challenge was intended to track the cutting edge in integer factorization. A primary application is for choosing the key length of the RSA public-key encryption scheme. Progress in this challenge should give an insight into
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https://en.wikipedia.org/wiki/Formal%20sum
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In mathematics, a formal sum, formal series, or formal linear combination may be:
In group theory, an element of a free abelian group, a sum of finitely many elements from a given basis set multiplied by integer coefficients.
In linear algebra, an element of a vector space, a sum of finitely many elements from a given basis set multiplied by real, complex, or other numerical coefficients.
In the study of series (mathematics), a sum of an infinite sequence of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum converges.
In the study of power series, a sum of infinitely many monomials with distinct positive integer exponents, again considered as an abstract object regardless of convergence.
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https://en.wikipedia.org/wiki/Tensor%20calculus
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In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).
Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold.
Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning.
Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus:In our subject of differential geometry, where you talk about manifolds, one difficulty is that the geometry is described by coordinates, but the coordinates do not have meaning. They are allowed to undergo transformation. And in order to handle this kind of situation, an important tool is the so-called tensor analysis, or Ricci calculus, which was new to mathematicians. In mathematics you have a function, you write down the function, you calculate, or you add, or you multiply, or you can differentiate. You have something very concret
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https://en.wikipedia.org/wiki/Reduce%20%28computer%20algebra%20system%29
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Reduce is a general-purpose computer algebra system geared towards applications in physics.
The development of the Reduce computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development under his direction.
Reduce is written entirely in its own LISP dialect called Portable Standard Lisp, expressed in an ALGOL-like syntax called RLISP. The latter is used as a basis for Reduce's user-level language.
Implementations of Reduce are available on most variants of Unix, Linux, Microsoft Windows, or Apple Macintosh systems by using an underlying Portable Standard Lisp or Codemist Standard LISP implementation. The Julia package Reduce.jl uses Reduce as a backend and implements its semantics in Julia style.
Reduce was open sourced in December 2008 and is available for free under a modified BSD license on SourceForge. Previously it had cost $695.
See also
Comparison of computer algebra systems
ALTRAN
REDUCE Meets CAMAL - REDUCE Computer Algebra System - J. P. Fitch
References
External links
Reduce wiki on SourceForge.
Anthony C. Hearn, Reduce User's Manual Version 3.8, February 2004. In HTML format.
Anthony C. Hearn, "Reduce: The First Forty Years", invited paper presented at the A3L Conference in Honor of the 60th Birthday of Volker Weispfenning, April 2005.
Andrey Grozin, "TeXmacs-Reduce interface", April 2012.
Computer algebra system software for Linux
Computer algebra sys
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https://en.wikipedia.org/wiki/The%20Genetical%20Theory%20of%20Natural%20Selection
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The Genetical Theory of Natural Selection is a book by Ronald Fisher which combines Mendelian genetics with Charles Darwin's theory of natural selection, with Fisher being the first to argue that "Mendelism therefore validates Darwinism" and stating with regard to mutations that "The vast majority of large mutations are deleterious; small mutations are both far more frequent and more likely to be useful", thus refuting orthogenesis. First published in 1930 by The Clarendon Press, it is one of the most important books of the modern synthesis, and helped define population genetics. It is commonly cited in biology books, outlining many concepts that are still considered important such as Fisherian runaway, Fisher's principle, reproductive value, Fisher's fundamental theorem of natural selection, Fisher's geometric model, the sexy son hypothesis, mimicry and the evolution of dominance. It was dictated to his wife in the evenings as he worked at Rothamsted Research in the day.
Contents
In the preface, Fisher considers some general points, including that there must be an understanding of natural selection distinct from that of evolution, and that the then-recent advances in the field of genetics (see history of genetics) now allowed this. In the first chapter, Fisher considers the nature of inheritance, rejecting blending inheritance, because it would eliminate genetic variance, in favour of particulate inheritance. The second chapter introduces Fisher's fundamental theorem of na
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https://en.wikipedia.org/wiki/Enigma
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Enigma may refer to:
Riddle, someone or something that is mysterious or puzzling
Biology
ENIGMA, a class of gene in the LIM domain
Computing and technology
Enigma (company), a New York–based data-technology startup
Enigma machine, a family of German electro-mechanical encryption machines
Enigma, the codename for Red Hat Linux 7.2
Enigma (DVB), the second generation of Enigma software
Film
Enigma (1982 film), a film starring Martin Sheen and Sam Neill
Enigma (2001 film), a film adapted from the Robert Harris novel
Enigma (2009 film), a short film by the Shumway Brothers
Literature
Enigma (novel), a 1995 novel by Robert Harris
Enigma (DC Comics), a DC Comics character
Enigma (Marvel Comics), a Marvel Comics character
Enigma (Vertigo), a title published by DC's imprint Vertigo
Enigma (manga), a 2010 manga published in Weekly Shōnen Jump
Enigma Cipher, a series from Boom! Studios
Enigma, a novel in The Trigon Disunity series by Michael P. Kube-McDowell
"Enigma" and "An Enigma", two poems by Edgar Allan Poe
The Riddler, DC comics character whose full name abbreviates to E. Nigma
Music
Enigma (German band), an electronic music project founded by Michael Cretu
Enigma (British band), a 1980s band
Enigma Records, an American rock and alternative record label in the 1980s
Enigma Variations, 14 variations composed by Edward Elgar
Albums
Enigma (Ill Niño album) (2008)
Enigma (Tak Matsumoto album) (2016)
Enigma (Keith Murray album) (1996)
Enigma (Aeon Zen album) (2013)
Songs
"Enig
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https://en.wikipedia.org/wiki/Gabriel%20Cramer
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Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. He was the son of physician Jean Cramer and Anne Mallet Cramer.
Biography
Cramer showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics at the University of Geneva.
In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli.
He published his best-known work in his forties. This included his treatise on algebraic curves (1750). It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position. (See Cramer's theorem (algebraic curves).) This led to the misconception that is Cramer's paradox, concerning the number of intersections of two curves compared to the number of points that determine a curve.
He edited the works of the two elder Bernoullis, and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746).
In 1750 he published Cramer's rule, giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of determinants implied by the system. This rule is still standard.
He did extensive travel throughout Europe in the late 1730s, which greatly influenced his works in mathematics. He died in 1752 at Bag
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https://en.wikipedia.org/wiki/STS-43
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STS-43, the ninth mission for Space Shuttle Atlantis, was a nine-day mission whose primary goal was launching the TDRS-E satellite (TDRS-5). The flight also tested an advanced heatpipe radiator for potential use on the then-future space station and conducted a variety of medical and materials science investigations.
Crew
Crew seating arrangements
Preparations and launch
The launch took place on August 2, 1991, 11:01:59 a.m. EDT. Launch was originally set for July 23, 1991, but was moved to July 24 to allow time to replace a faulty integrated electronics assembly that controls orbiter/external tank separation. The mission was postponed again about five hours before liftoff on July 24, 1991, due to a faulty main engine controller on the number three main engine. The controller was replaced and retested; launch was reset for August 1, 1991. Liftoff set for 11:01 a.m. delayed due to cabin pressure vent valve reading and postponed at 12:28 p.m. due to unacceptable return-to-launch site weather conditions. Launch finally occurred on August 2, 1991, without further delays.
Mission highlights
The primary payload, TDRS-E, attached to an Inertial Upper Stage (IUS), was deployed about six hours into flight, and the IUS propelled the satellite into geosynchronous orbit. TDRS-5 became the fourth member of the orbiting TDRS cluster. Secondary payloads were Space Station Heat Pipe Advanced Radiator Element (SHARE II); Shuttle Solar Backscatter Ultra-Violet (SSBUV) instrument; Tank Pr
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https://en.wikipedia.org/wiki/Joseph%20Hooton%20Taylor%20Jr.
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Joseph Hooton Taylor Jr. (born March 29, 1941) is an American astrophysicist and Nobel Prize laureate in Physics for his discovery with Russell Alan Hulse of a "new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation."
Early life and education
Taylor was born in Philadelphia to Joseph Hooton Taylor Sr. and Sylvia Evans Taylor, both of whom had Quaker roots for many generations, and grew up in Cinnaminson Township, New Jersey. He attended the Moorestown Friends School in Moorestown Township, New Jersey, where he excelled in math.
He received a B.A. in physics at Haverford College in 1963, and a Ph.D. in astronomy at Harvard University in 1968. After a brief research position at Harvard, Taylor went to the University of Massachusetts Amherst, eventually becoming Professor of Astronomy and Associate Director of the Five College Radio Astronomy Observatory.
Taylor's thesis work was on lunar occultation measurements. About the time he completed his Ph.D., Jocelyn Bell (who is also a Quaker) discovered the first radio pulsars with a telescope near Cambridge, England.
Career
Taylor immediately went to the National Radio Astronomy Observatory's telescopes in Green Bank, West Virginia, and participated in the discovery of the first pulsars discovered outside Cambridge. Since then, he has worked on all aspects of pulsar astrophysics.
In 1974, Hulse and Taylor discovered the first pulsar in a binary system, named PSR B1913+16 after its posi
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https://en.wikipedia.org/wiki/Steven%20Hawley
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Steven Alan Hawley (born December 12, 1951) is a former NASA astronaut who flew on five U.S. Space Shuttle flights. He is professor of physics and astronomy and director of engineering physics at the University of Kansas.
Early life
Hawley was born December 12, 1951, in Ottawa, Kansas, to Dr. and Mrs. Bernard Hawley. One of Hawley's brothers, John F. Hawley, was a theoretical astrophysicist at the University of Virginia and shared the Shaw Prize in Astronomy in 2013.
Hawley graduated from Salina High School Central, Salina, Kansas, in 1969; he regards Salina as his home town. Hawley attended the University of Kansas, graduating with highest distinction in 1973 with Bachelor of Science degrees in Physics and in Astronomy. He spent three summers employed as a research assistant: 1972 at the U.S. Naval Observatory in Washington, D.C., and 1973 and 1974 at the National Radio Astronomy Observatory in Green Bank, West Virginia. He attended graduate school at Lick Observatory, University of California, Santa Cruz, graduating in 1977 with a Doctorate in Astronomy and Astrophysics.
Career
Hawley's research involved spectrophotometry of gaseous nebulae and emission-line galaxies, with particular emphasis on chemical abundance determinations for these objects. The results of his research have been published in major astronomical journals. Prior to his selection by NASA in 1978, Hawley was a post-doctoral research associate at Cerro Tololo Inter-American Observatory in La Serena, Ch
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https://en.wikipedia.org/wiki/Russell%20Alan%20Hulse
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Russell Alan Hulse (born November 28, 1950) is an American physicist and winner of the Nobel Prize in Physics, shared with his thesis advisor Joseph Hooton Taylor Jr., "for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation".
Biography
Hulse was born in New York City and graduated from the Bronx High School of Science and the Cooper Union. He received his PhD in physics from the University of Massachusetts Amherst in 1975.
While working on his PhD dissertation, he was a scholar in 1974 at the Arecibo Observatory in Puerto Rico of Cornell University. There he worked with Taylor on a large-scale survey for pulsars. It was this work that led to the discovery of the first binary pulsar.
In 1974, Hulse and Taylor discovered binary pulsar PSR B1913, which is made up of a pulsar and black companion star. Neutron star rotation emits impulses that are extremely regular and stable in the radio wave region and is nearby condensed material body gravitation (non-detectable in the visible field). Hulse, Taylor, and other colleagues have used this first binary pulsar to make high-precision tests of general relativity, demonstrating the existence of gravitational radiation. An approximation of this radiant energy is described by the formula of the quadrupolar radiation of Albert Einstein (1918).
In 1979, researchers announced measurements of small acceleration effects of the orbital movements of a pulsar. This was initia
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https://en.wikipedia.org/wiki/Mario%20Molina
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Mario José Molina Henríquez (19 March 19437 October 2020) was a Mexican physical chemist. He played a pivotal role in the discovery of the Antarctic ozone hole, and was a co-recipient of the 1995 Nobel Prize in Chemistry for his role in discovering the threat to the Earth's ozone layer from chlorofluorocarbon (CFC) gases. He was the first Mexican-born scientist to receive a Nobel Prize in Chemistry and the third Mexican-born person to receive a Nobel prize.
In his career, Molina held research and teaching positions at University of California, Irvine, California Institute of Technology, Massachusetts Institute of Technology, University of California, San Diego, and the Center for Atmospheric Sciences at the Scripps Institution of Oceanography. Molina was also Director of the Mario Molina Center for Energy and Environment in Mexico City. Molina was a climate policy advisor to the President of Mexico, Enrique Peña Nieto.
Early life
Molina was born in Mexico City to Roberto Molina Pasquel and Leonor Henríquez. His father was a lawyer and diplomat who served as an ambassador to Ethiopia, Australia and the Philippines. His mother was a family manager. With considerably different interests than his parents, Mario Molina went on to make one of the biggest discoveries in environmental science.
Mario Molina attended both elementary and primary school in Mexico. However, before even attending high school, Mario Molina had developed a deep interest in chemistry. As a child he convert
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https://en.wikipedia.org/wiki/BIOSCI
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BIOSCI, also known as Bionet, is a set of electronic communication forum used by life scientists around the world. It includes the Bionet Usenet newsgroups and parallel e-mail lists, with public archives since 1992 at www.bio.net. BIOSCI/Bionet provides public, open access biology news and discussion for areas such as molecular biology methods and reagents, bioinformatics software and computational biology, toxicology, and several organism communities including yeast, C.elegans and annelida (worms), the plant arabidopsis, fruitfly, maize (corn), and others.
BIOSCI/Bionet was started as part of the GenBank public biosequence database project by Intelligenetics at Stanford University in the mid-1980s, in collaboration with Martin Bishop and Michael Ashburner in the University of Cambridge. It latter moved to the United Kingdom's MRC Rosalind Franklin Centre for Genomics Research (RFCGR). In 2005, with the closing of RFCGR, BIOSCI/Bionet moved to Indiana University Biology Department's IUBio Archive.
As one of the earliest bioinformatics community projects on the Internet, GenBank acquired the bio.net domain and the Usenet hierarchy of Bionet for promoting open access communications among bioscientists, in conjunction with public biology data distribution.
Michael Ashburner, co-founder of BIOSCI with Dave Kristofferson of GenBank (Intelligenetics), writes of its origins ... in the early 1980s, Martin Bishop and I ran an email news service for a sequence analysis service
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https://en.wikipedia.org/wiki/Henderson%E2%80%93Hasselbalch%20equation
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In chemistry and biochemistry, the Henderson–Hasselbalch equation
relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, Ka, of acid and the ratio of the concentrations, of the acid and its conjugate base in an equilibrium.
For example, the acid may be acetic acid
The Henderson–Hasselbalch equation can be used to estimate the pH of a buffer solution by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA.
The equation can also be applied to bases by specifying the protonated form of the base as the acid. For example, with an amine,
Derivation, assumptions and limitations
A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate.
The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, Ka of the acid, and the concentrations of the species in solution.
To derive the equation a number of simplifying assumptions have to be made. (pdf)
Assumption 1: The acid, HA, is monobasic and dissociates according to the equations
CA is the analytical concentration of the acid and CH is the concentration the hydrogen ion that has been added to the solution. The self-dissociation of water is ignored. A quantity in square brackets, [X], represents the c
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https://en.wikipedia.org/wiki/Invagination
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Invagination is the process of a surface folding in on itself to form a cavity, pouch or tube. In developmental biology, invagination is a mechanism that takes place during gastrulation. This mechanism or cell movement happens mostly in the vegetal pole. Invagination consists of the folding of an area of the exterior sheet of cells towards the inside of the blastula. In each organism, the complexity will be different depending on the number of cells. Invagination can be referenced as one of the steps of the establishment of the body plan. The term, originally used in embryology, has been adopted in other disciplines as well.
There is more than one type of movement for invagination. Two common types are axial and orthogonal. The difference between the production of the tube formed in the cytoskeleton and extracellular matrix. Axial can be formed at a single point along the axis of a surface. Orthogonal is linear and trough.
Biology
Invagination is the morphogenetic processes by which an embryo takes form, and is the initial step of gastrulation, the massive reorganization of the embryo from a simple spherical ball of cells, the blastula, into a multi-layered organism, with differentiated germ layers: endoderm, mesoderm, and ectoderm. More localized invaginations also occur later in embryonic development,
The inner membrane of a mitochondrion invaginates to form cristae, thus providing a much greater surface area to accommodate the protein complexes and other participants
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https://en.wikipedia.org/wiki/Oxidase
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In biochemistry, an oxidase is an enzyme that catalyzes oxidation-reduction reactions, especially one involving dioxygen (O2) as the electron acceptor. In reactions involving donation of a hydrogen atom, oxygen is reduced to water (H2O) or hydrogen peroxide (H2O2). Some oxidation reactions, such as those involving monoamine oxidase or xanthine oxidase, typically do not involve free molecular oxygen.
The oxidases are a subclass of the oxidoreductases.
Examples
An important example is cytochrome c oxidase, the key enzyme that allows the body to employ oxygen in the generation of energy and the final component of the electron transfer chain. Other examples are:
Glucose oxidase
Monoamine oxidase
Cytochrome P450 oxidase
NADPH oxidase
Xanthine oxidase
L-gulonolactone oxidase
Laccase
Lysyl oxidase
Polyphenol oxidase
Sulfhydryl oxidase. This enzyme oxidises thiol groups.
Oxidase test
In microbiology, the oxidase test is used as a phenotypic characteristic for the identification of bacterial strains; it determines whether a given bacterium produces cytochrome oxidases (and therefore utilizes oxygen with an electron transfer chain).
The test is used to determine whether a bacterium is an aerobe or anaerobe. However a bacterium that is Oxidase negative is not necessarily anaerobic, instead showing the bacterium does not possess cytochrome c oxidase.
References
External links
Catalase & Oxidase tests video
Oxidoreductases
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https://en.wikipedia.org/wiki/Swallowtail
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Swallowtail may refer to:
Swallowtail catastrophe or swallowtail surface, a singularity occurring in the part of mathematics called catastrophe theory
Swallow-tail coat, a formal tailcoat worn traditionally as part of the white tie dress code
Swallowtail butterfly, large colorful butterflies from the family Papilionidae
Swallowtail (film), 1996 film directed by Shunji Iwai
Swallowtail (flag), a term in vexillology
Swallowtail joint in woodworking, see Dovetail joint
The Swallow's Tail, a painting by Salvador Dalí, inspired by the swallowtail catastrophe
Swallowtail, a butler café in Tokyo, Japan
Swallowtail, a Wolf Alice song from their debut album My Love Is Cool
See also
Swallowtail Butterfly (Ai no Uta), the theme song for the film Swallowtail
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https://en.wikipedia.org/wiki/Population%20dynamics
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Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems.
History
Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope of mathematical biology has greatly expanded.
The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model. According to Malthus, assuming that the conditions (the environment) remain constant (ceteris paribus), a population will grow (or decline) exponentially. This principle provided the basis for the subsequent predictive theories, such as the demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model.
A more general model formulation was proposed by F. J. Richards in 1959, further expanded by Simon Hopkins, in which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. The Lotka–Volterra predator-prey equations are another famous example, as well as the alternative Arditi–Ginzburg equations.
Logistic function
Simplified population models usually start with four key variables (four demographic processes) including death, birth, immigration, and emigration. Mathematical models used to calculate changes in population de
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https://en.wikipedia.org/wiki/John%20Boardman%20%28physicist%29
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Jack Melton Boardman, commonly known as John Boardman, (born September 8, 1932) is an American physicist. He is a former professor of physics at Brooklyn College; a noted science fiction fan, author and fanzine publisher; and a gaming authority.
Academic career
Boardman earned his BA at the University of Chicago in 1952 and his MS from Iowa State University in 1956. He then attended Florida State University to begin his doctoral studies. However, he was expelled in 1957 due to his involvement with the Inter-Civic Council and more specifically for inviting three black Florida A&M exchange students to a Christmas party.
He ultimately received his PhD in physics at Syracuse University in 1962; his doctoral thesis was titled Quantization of the General Theory of Relativity. His publications include "Spherical Gravitational Waves" (a collaboration with Peter Bergmann, former research assistant to Albert Einstein), "Contributions to the Quantization Problem in General Relativity", and "The Normal Modes Of A Hanging Oscillator Of Order N".
Boardman and gaming
Boardman was involved in early play-by-mail (PBM) for the Diplomacy game, and for a small fee he would send copies of each player's turns to every other player involved in a game. He is one of the most noted figures in the game of Diplomacy, having established the original play-by-mail setup in 1961, and also the system of numbering each game for statistical purposes. These numbers, known as Boardman Numbers, include the y
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https://en.wikipedia.org/wiki/Hodge%20theory
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In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic.
The theory was developed by Hodge in the 1930s to study algebraic geometry, and it built on the work of Georges de Rham on de Rham cohomology. It has major applications in two settings: Riemannian manifolds and Kähler manifolds. Hodge's primary motivation, the study of complex projective varieties, is encompassed by the latter case. Hodge theory has become an important tool in algebraic geometry, particularly through its connection to the study of algebraic cycles.
While Hodge theory is intrinsically dependent upon the real and complex numbers, it can be applied to questions in number theory. In arithmetic situations, the tools of p-adic Hodge theory have given alternative proofs of, or analogous results to, classical Hodge theory.
History
The field of algebraic topology was still nascent in the 1920s. It had not yet developed the notion of cohomology, and the interaction between differential forms and topology was poorly understood. In 1928, Élie Cartan published a note entitled Sur les nombres de Betti des espaces de groupes clos in which he suggested, but did not prove, that di
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https://en.wikipedia.org/wiki/Starvation%20%28computer%20science%29
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In computer science, resource starvation is a problem encountered in concurrent computing where a process is perpetually denied necessary resources to process its work. Starvation may be caused by errors in a scheduling or mutual exclusion algorithm, but can also be caused by resource leaks, and can be intentionally caused via a denial-of-service attack such as a fork bomb.
When starvation is impossible in a concurrent algorithm, the algorithm is called starvation-free, lockout-freed or said to have finite bypass. This property is an instance of liveness, and is one of the two requirements for any mutual exclusion algorithm; the other being correctness. The name "finite bypass" means that any process (concurrent part) of the algorithm is bypassed at most a finite number times before being allowed access to the shared resource.
Scheduling
Starvation is usually caused by an overly simplistic scheduling algorithm. For example, if a (poorly designed) multi-tasking system always switches between the first two tasks while a third never gets to run, then the third task is being starved of CPU time. The scheduling algorithm, which is part of the kernel, is supposed to allocate resources equitably; that is, the algorithm should allocate resources so that no process perpetually lacks necessary resources.
Many operating system schedulers employ the concept of process priority. A high priority process A will run before a low priority process B. If the high priority process (process A)
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https://en.wikipedia.org/wiki/Ramification%20group
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In number theory, more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information on the ramification phenomena of the extension.
Ramification theory of valuations
In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains.
The structure of the set of extensions is known better when L/K is Galois.
Decomposition group and inertia group
Let (K, v) be a valued field and let L be a finite Galois extension of K. Let Sv be the set of equivalence classes of extensions of v to L and let G be the Galois group of L over K. Then G acts on Sv by σ[w] = [w ∘ σ] (i.e. w is a representative of the equivalence class [w] ∈ Sv and [w] is sent to the equivalence class of the composition of w with the automorphism ; this is independent of the choice of w in [w]). In fact, this action is transitive.
Given a fixed extension w of v to L, the decomposition group of w is the stabilizer subgroup Gw of [w], i.e. it is the subgroup of G consisting of all elements that fix the equivalence class [w] ∈ Sv.
Let mw denote the maximal ideal of w inside the valuation ring Rw of w. The inertia group of w is the subgroup Iw of Gw consisting of elements σ such that σx ≡ x (mod mw) for all x in Rw. In other words, Iw consists of the elements of the decomposit
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https://en.wikipedia.org/wiki/Of%20Moths%20and%20Men
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Of Moths and Men is a book by journalist Judith Hooper about the Oxford University ecological genetics school led by E.B. Ford. The book specifically concerns Bernard Kettlewell's experiments on the peppered moth which were intended as experimental validation of evolution. She highlights supposed problems with the methodology of Kettlewell's experiments and suggests that these issues could invalidate the results obtained, ignoring or disparaging evidence supporting natural selection while repeatedly implying that Kettlewell and his colleagues committed fraud or made careless errors. Subject matter experts have described the book as presenting a "conspiracy theory" with "errors, misrepresentations, misinterpretations and falsehoods". The evolutionary biologist Michael Majerus spent the last 7 years of his life systematically repeating Kettlewell's experiments, demonstrating that Kettlewell had in fact been correct.
Allegations of poor experimental practice
Hooper alleges several flaws in experimental methodology, including gluing the moths in place on parts of trees where they would not naturally settle, feeding birds heavily enough to condition them to expect feeding at that point, artificially boosting recapture rates, altering experiments (unconsciously) to favour the expected outcome, and errors in statistical analysis.
The historian of biology David Rudge has carefully reexamined the records upon which Hooper's argument is based. His conclusions were that her histor
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https://en.wikipedia.org/wiki/Magnetocrystalline%20anisotropy
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In physics, a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others. These directions are usually related to the principal axes of its crystal lattice. It is a special case of magnetic anisotropy. In other words, the excess energy required to magnetize a specimen in a particular direction over that required to magnetize it along the easy direction is called crystalline anisotropy energy.
Causes
The spin-orbit interaction is the primary source of magnetocrystalline anisotropy. It is basically the orbital motion of the electrons which couples with crystal electric field giving rise to the first order contribution to magnetocrystalline anisotropy. The second order arises due to the mutual interaction of the magnetic dipoles. This effect is weak compared to the exchange interaction and is difficult to compute from first principles, although some successful computations have been made.
Practical relevance
Magnetocrystalline anisotropy has a great influence on industrial uses of ferromagnetic materials. Materials with high magnetic anisotropy usually have high coercivity, that is, they are hard to demagnetize. These are called "hard" ferromagnetic materials and are used to make permanent magnets. For example, the high anisotropy of rare-earth metals is mainly responsible for the strength of rare-earth magnets. During manufacture of magnets, a powerful magnetic field aligns the micr
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https://en.wikipedia.org/wiki/TGN
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TGN may refer to:
Tarragona, abbreviation of the city of Tarragona, in Catalonia
Thai Global Network, a Thai satellite television channel
Texas Government Newsletter, for college students
Tyco Global Network, fiber optic network by Tyco International
Trans Golgi network in biology
IEEE 802.11n Task Group N
Thyroglobulin, a protein
Getty Thesaurus of Geographic Names
TGN (AM) radio station, Guatemala
Latrobe Regional Airport, IATA airport code "TGN"
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https://en.wikipedia.org/wiki/Hemostasis
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In biology, hemostasis or haemostasis is a process to prevent and stop bleeding, meaning to keep blood within a damaged blood vessel (the opposite of hemostasis is hemorrhage). It is the first stage of wound healing. This involves coagulation, which changes blood from a liquid to a gel. Intact blood vessels are central to moderating blood's tendency to form clots. The endothelial cells of intact vessels prevent blood clotting with a heparin-like molecule and thrombomodulin, and prevent platelet aggregation with nitric oxide and prostacyclin. When endothelium of a blood vessel is damaged, the endothelial cells stop secretion of coagulation and aggregation inhibitors and instead secrete von Willebrand factor, which initiate the maintenance of hemostasis after injury. Hemostasis involves three major steps:
vasoconstriction
temporary blockage of a hole in a damaged blood vessel by a platelet plug
blood coagulation (formation of fibrin clots)
These processes seal the injury or hole until tissues are healed.
Etymology and pronunciation
The word hemostasis (, sometimes ) uses the combining forms and , Neo-Latin from Ancient Greek (similar to ), meaning "blood", and , meaning "stasis", yielding "motionlessness or stopping of blood".
Steps of mechanism
Hemostasis occurs when blood is present outside of the body or blood vessels. It is the innate response for the body to stop bleeding and loss of blood. During hemostasis three steps occur in a rapid sequence. Vascular spasm
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https://en.wikipedia.org/wiki/Cancer%20Cell%20%28journal%29
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Cancer Cell is a peer-reviewed scientific journal scientific journal that publishes articles that provide major advances in cancer research and oncology. The journal considers manuscripts that answer important questions relevant to naturally occurring cancers. Areas covered include basic cancer biology, therapeutic development, translational research, cancer model development, multi-omics and computational biology. Cancer Cell is also interested in publishing clinical investigations, in particular those that lead to establishing new paradigms in the treatment, diagnosis, or prevention of cancers; those that provide important insights into cancer biology beyond what has been revealed by preclinical studies; and those that are mechanism-based proof-of-principle clinical studies.
Cancer Cell is internationally regarded as one of the top cancer research and oncology journals. According to the Journal Citation Reports, the 2022 impact factor of the journal is 50.3. It is part of the Cell Press portfolio, which is owned by Elsevier. Issues are published monthly in print and online versions. All content becomes available for free one year after publication. In January 2021, Cancer Cell became a Transformative Journal as part of Elsevier's efforts to increase Open Access content.
Cancer Cell publishes Research, Review, and Perspective articles, in addition to opinion pieces such as Letters, Commentaries, Previews, Spotlight, and Voices. The journal often publishes a yearly special
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https://en.wikipedia.org/wiki/Poisson%20summation%20formula
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In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. And conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. The Poisson summation formula was discovered by Siméon Denis Poisson and is sometimes called Poisson resummation.
Forms of the equation
Consider an aperiodic function with Fourier transform alternatively designated by and
The basic Poisson summation formula is:
Also consider periodic functions, where parameters and are in the same units as :
Then is a special case (P=1, x=0) of this generalization:
which is a Fourier series expansion with coefficients that are samples of the function Similarly:
also known as the important Discrete-time Fourier transform.
The Poisson summation formula can also be proved quite conceptually using the compatibility of Pontryagin duality with short exact sequences such as
Applicability
holds provided is a continuous integrable function which satisfies
for some and every Note that such is uniformly continuous, this together with the decay assumption on , show that the series defining converges uniformly to a continuous function. holds in the
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https://en.wikipedia.org/wiki/Framhaldssk%C3%B3linn%20%C3%AD%20Vestmannaeyjum
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Framhaldsskólinn í Vestmannaeyjum, the comprehensive secondary school of Vestmannaeyjar, Iceland, was founded 1979 when the mechanical engineering, common trades (is. iðnskóli) and the higher education department of the secondary school merged into one.
Then in 1997, it also took over the school of maritime navigation.
Currently there are seven departments in the school: Natural sciences, social sciences, linguistics, job training (for the disabled), medical aide training, electrical engineering and mechanical engineering.
The school is also currently used as the teaching facility for the Vestmannaeyjar department of the University of Iceland and has hosted many remote lectures, to Ísafjörður and Bíldudalur as well as a few other countries.
Education in Iceland
Gymnasiums in Iceland
Educational institutions established in 1979
1979 establishments in Iceland
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https://en.wikipedia.org/wiki/Diophantine%20geometry
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In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Diophantine geometry is part of the broader field of arithmetic geometry.
Four theorems in Diophantine geometry that are of fundamental importance include:
Mordell–Weil theorem
Roth's theorem
Siegel's theorem
Faltings's theorem
Background
Serge Lang published a book Diophantine Geometry in the area in 1962, and by this book he coined the term "Diophantine geometry". The traditional arrangement of material on Diophantine equations was by degree and number of variables, as in Mordell's Diophantine Equations (1969). Mordell's book starts with a remark on homogeneous equations f = 0 over the rational field, attributed to C. F. Gauss, that non-zero solutions in integers (even primitive lattice points) exist if non-zero rational solutions do, and notes a caveat of L. E. Dickson, which is about parametric solutions. The Hilbert–Hurwitz result from 1890 reducing the Diophantine geometry of curves of genus 0 to degrees 1 and 2 (conic sections) occurs in Chapter 17, as does Mordell's conjecture. Siegel's theorem on integral points occurs in Chapter 28. Mordell's theorem on the finite generation of the group of rational points on an elliptic curve is in Chapter 16, and integer points on the Mordell curve in Chapter 26.
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https://en.wikipedia.org/wiki/Inverse%20kinematics
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In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics. However, the reverse operation is, in general, much more challenging.
Inverse kinematics is also used to recover the movements of an object in the world from some other data, such as a film of those movements, or a film of the world as seen by a camera which is itself making those movements. This occurs, for example, where a human actor's filmed movements are to be duplicated by an animated character.
Robotics
In robotics, inverse kinematics makes use of the kinematics equations to determine the joint parameters that provide a desired configuration (position and rotation) for each of the robot's end-effectors. This is important because robot tasks are performed with the end effectors, while control effort applies to the joints. Determining the movement of a robot so that its end-effectors move from an initial configuration to a desired configuration is known as motion planning. Inverse kinematics transforms the motion plan into j
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https://en.wikipedia.org/wiki/Crawl
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Crawl, The Crawl, or crawling may refer to:
Biology
Crawling (human), any of several types of human quadrupedal gait
Limbless locomotion, the movement of limbless animals over the ground
Undulatory locomotion, a type of motion characterized by wave-like movement patterns that act to propel an animal forward
Gaming
Crawl (video game), a 2014 roguelike indie video game
Dungeon crawl, a type of scenario in fantasy role-playing games
Linley's Dungeon Crawl or Crawl, a 1997 roguelike computer game
Dungeon Crawl Stone Soup, an ongoing open source fork of Linley's Dungeon Crawl
Music
The Crawl, backing band for Mike Morgan
Albums
Crawl (album), by Deen, 2010
Crawl, by Coffin Break, or the title song, 1991
Crawl (Entombed EP), 1991
Crawl (Laughing Hyenas EP), 1992
The Crawl (Louis Hayes album), 1990
The Crawl (Mickey Tucker album) or the title song, 1980
Songs
"Crawl" (Atlas song), 2007
"Crawl" (Childish Gambino song), 2014
"Crawl" (Chris Brown song), 2009
"Crawl" (Kings of Leon song), 2009
"Crawling" (song), by Linkin Park, 2001
"Crawl", by Alkaline Trio from From Here to Infirmary, 2001
"Crawl", by Anthrax from Worship Music, 2011
"Crawl", by Breaking Benjamin from Dear Agony, 2009
"Crawl", by Damageplan from New Found Power, 2004
"Crawl", by Miss May I from Shadows Inside, 2017
"Crawl", by Norman Iceberg from Person(a), 1987
"Crawl", by Soul Asylum from Let Your Dim Light Shine, 1995
"Crawl", by Stabbing Westward from Dead and Gone, 2020
"Crawl",
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https://en.wikipedia.org/wiki/Yukawa%20potential
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In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form:
where is a magnitude scaling constant, i.e. is the amplitude of potential, is the mass of the particle, is the radial distance to the particle, and is another scaling constant, so that is the approximate range. The potential is monotonically increasing in and it is negative, implying the force is attractive. In the SI system, the unit of the Yukawa potential is (1/meters).
The Coulomb potential of electromagnetism is an example of a Yukawa potential with the factor equal to 1, everywhere. This can be interpreted as saying that the photon mass is equal to 0. The photon is the force-carrier between interacting, charged particles.
In interactions between a meson field and a fermion field, the constant is equal to the gauge coupling constant between those fields. In the case of the nuclear force, the fermions would be a proton and another proton or a neutron.
History
Prior to Hideki Yukawa's 1935 paper, physicists struggled to explain the results of James Chadwick's atomic model, which consisted of positively charged protons and neutrons packed inside of a small nucleus, with a radius on the order of 10−14 meters. Physicists knew that electromagnetic forces at these lengths would cause these protons to repel each other and for the nucleus to fall apart. Thus ca
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https://en.wikipedia.org/wiki/Charles%20Fefferman
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Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contributions to mathematical analysis.
Early life and education
Fefferman was born to a Jewish family, in Washington, DC. Fefferman was a child prodigy. Fefferman entered the University of Maryland at age 14, and had written his first scientific paper by the age of 15. He graduated with degrees in math and physics at 17, and earned his PhD in mathematics three years later from Princeton University, under Elias Stein. His doctoral dissertation was titled "Inequalities for strongly singular convolution operators". Fefferman achieved a full professorship at the University of Chicago at the age of 22, making him the youngest full professor ever appointed in the United States.
Career
At the age of 25, he returned to Princeton as a full professor, becoming the youngest person to be promoted to the title. He won the Alan T. Waterman Award in 1976 (the first person to get the award) and the Fields Medal in 1978 for his work in mathematical analysis, specifically convergence and divergence. He was elected to the National Academy of Sciences in 1979. He was appointed the Herbert Jones Professor at Princeton in 1984.
In addition to the above, his honors include the Salem Prize in 1971, the Bergman Prize in 1992, the Bôcher Memorial Prize in 2008, and
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https://en.wikipedia.org/wiki/Remainder
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In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor.
Alternatively, a remainder is also what is left after subtracting one number from another, although this is more precisely called the difference. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression "the rest" as in "Give me two dollars back and keep the rest." However, the term "remainder" is still used in this sense when a function is approximated by a series expansion, where the error expression ("the rest") is referred to as the remainder term.
Integer division
Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that and . The number q is called the quotient, while r is called the remainder.
(For a proof of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see division algorithm.)
The remainder, as defined above, is called the least positive remainder or simply the remainder. The integer a is either a multiple of d, or lies in the interval between consecutive multiples of d, n
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https://en.wikipedia.org/wiki/Radon%20transform
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In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes (integrating over lines is known as the X-ray transform). It was later generalized to higher-dimensional Euclidean spaces and more broadly in the context of integral geometry. The complex analogue of the Radon transform is known as the Penrose transform. The Radon transform is widely applicable to tomography, the creation of an image from the projection data associated with cross-sectional scans of an object.
Explanation
If a function represents an unknown density, then the Radon transform represents the projection data obtained as the output of a tomographic scan. Hence the inverse of the Radon transform can be used to reconstruct the original density from the projection data, and thus it forms the mathematical underpinning for tomographic reconstruction, also known as iterative reconstruction.
The Radon transform data is often called a sinogram because the Radon transform of an off-center point source is a sinusoid. Consequently, the Radon transform of a number of small obj
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https://en.wikipedia.org/wiki/Norman%20Ramsey%20Jr.
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Norman Foster Ramsey Jr. (August 27, 1915 – November 4, 2011) was an American physicist who was awarded the 1989 Nobel Prize in Physics, for the invention of the separated oscillatory field method (see Ramsey Interferometry) which had important applications in the construction of atomic clocks. A physics professor at Harvard University for most of his career, Ramsey also held several posts with such government and international agencies as NATO and the United States Atomic Energy Commission. Among his other accomplishments are helping to found the United States Department of Energy's Brookhaven National Laboratory and Fermilab.
Early life
Norman Foster Ramsey Jr. was born in Washington, D.C., on August 27, 1915, to Minna Bauer Ramsey, an instructor at the University of Kansas, and Norman Foster Ramsey, a 1905 graduate of the United States Military Academy at West Point and an officer in the Ordnance Department who rose to the rank of brigadier general during World War II, commanding the Rock Island Arsenal. He was raised as an Army brat, frequently moving from post to post, and lived in France for a time when his father was Liaison Officer with the Direction d'Artillerie and Assistant Military Attaché. This allowed him to skip a couple of grades along the way, so that he graduated from Leavenworth High School in Leavenworth, Kansas, at the age of 15.
Ramsey's parents hoped that he would go to West Point, but at 15, he was too young to be admitted. He was awarded a scholar
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https://en.wikipedia.org/wiki/Hausdorff%20measure
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In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and their Hausdorff dimensions. It is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in or, more generally, in any metric space.
The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite. Likewise, the one-dimensional Hausdorff measure of a simple curve in is equal to the length of the curve, and the two-dimensional Hausdorff measure of a Lebesgue-measurable subset of is proportional to the area of the set. Thus, the concept of the Hausdorff measure generalizes the Lebesgue measure and its notions of counting, length, and area. It also generalizes volume. In fact, there are d-dimensional Hausdorff measures for any d ≥ 0, which is not necessarily an integer. These measures are fundamental in geometric measure theory. They appear naturally in harmonic analysis or potential theory.
Definition
Let be a metric space. For any subset , let denote its diameter, that is
Let be any subset of and a real number. Define
where the infimum is over all countable covers of by sets satisfying .
Note that is monotone nonincreasing in since the larger is, the more collections of sets are permitted, making the infimum not larger. Thus, exists but may be infinite. Let
It can be seen that is an outer measure (more pre
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https://en.wikipedia.org/wiki/STS-55
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STS-55, or Deutschland 2 (D-2), was the 55th overall flight of the NASA Space Shuttle and the 14th flight of Shuttle Columbia. This flight was a multinational Spacelab flight involving 88 experiments from eleven different nations. The experiments ranged from biology sciences to simple Earth observations.
Crew
Backup crew
Mission highlights
Columbia carried to orbit the second reusable German Spacelab D-2 and demonstrated the shuttle's ability for international cooperation, exploration, and scientific research in space. The Spacelab module and an exterior experiment support structure contained in Columbias payload bay comprised the Spacelab D-2 payload. The first German Spacelab flight, D-1, flew Shuttle mission STS-61-A in October 1985. The United States and Germany gained valuable experience for future space station operations.
The D-2 mission, as it was commonly called, augmented the German microgravity research program started by the D-1 mission. The German Aerospace Center (DLR) had been tasked by the German Space Agency (DARA - Deutsche Agentur für Raumfahrtangelegenheiten) to conduct the second mission. DLR, NASA, the European Space Agency (ESA), and agencies in France and Japan contributed to D-2's scientific program. Eleven nations participated in the experiments. Of the 88 experiments conducted on the D-2 mission, four were sponsored by NASA.
The crew worked in two shifts around-the-clock to complete investigations into the areas of fluid physics, materials sci
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https://en.wikipedia.org/wiki/Nicholas%20Metropolis
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Nicholas Constantine Metropolis (Greek: ; June 11, 1915 – October 17, 1999) was a Greek-American physicist.
Metropolis received his BSc (1937) and PhD in physics (1941, with Robert Mulliken) at the University of Chicago. Shortly afterwards, Robert Oppenheimer recruited him from Chicago, where he was collaborating with Enrico Fermi and Edward Teller on the first nuclear reactors, to the Los Alamos National Laboratory.
He arrived in Los Alamos in April 1943, as a member of the original staff of fifty scientists. He came back to Los Alamos in 1948 to lead the group in the Theoretical Division that designed and built the MANIAC I computer in 1952 that was modeled on the IAS machine, and the MANIAC II in 1957.
Early life and education
Nicolas Metropolis was born on June 11, 1915, in Chicago, US. Metropolis received his BSc (1936) and PhD in chemical physics (1941) at the University of Chicago. During his PhD he worked with Robert Mulliken. After graduation, he worked as an instructor at the University of Chicago with James Franck. Shortly afterwards, in 1943, Robert Oppenheimer recruited him from Chicago for the Manhattan Project, where he worked in Harold C. Urey's group. Later he joined University of Chicago Metallurgical Laboratory and worked under Edward Teller's supervision, who encouraged him to move into theoretical physics. At Los Alamos Metropolis worked together with Richard Feynman on "electromechanical devices used for hand computations".
After World War II
After
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https://en.wikipedia.org/wiki/Frederick%20Guthrie
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Frederick Guthrie FRS FRSE (15 October 1833 – 21 October 1886) was a British physicist, chemist, and academic author.
He was the son of Alexander Guthrie, a London tradesman, and the younger brother of mathematician Francis Guthrie. Along with William Fletcher Barrett he founded the Physical Society of London (now the Institute of Physics) in 1874 and was president of the society from 1884 until 1886. He believed that science should be based on experimentation rather than discussion.
Academic career
His academic career started at University College, London, where he studied for three years. He studied chemistry under Thomas Graham and Alexander William Williamson and mathematics under Augustus De Morgan. In 1852, he submitted his brother Francis's observations to De Morgan.
In 1854 Guthrie went to Heidelberg to study under Robert Bunsen and then in 1855 obtained a PhD at the University of Marburg under Adolph Wilhelm Hermann Kolbe.
In 1856 he joined Edward Frankland, professor of chemistry at Owens College, Manchester. In 1859 he went to the University of Edinburgh.
Guthrie synthesized mustard gas in 1860 from ethylene and sulfur dichloride. Gutherie probably was not the first to synthesize mustard gas, but he was among the first to document its toxic effects. Gutherie did his mustard gas synthesis almost simultaneously as Albert Niemann, who also synthesized mustard gas and noted its toxic effects in his own experiments. Both Gutherie and Niemann published their finding
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https://en.wikipedia.org/wiki/Algebraic%20torus
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In mathematics, an algebraic torus, where a one dimensional torus is typically denoted by , , or , is a type of commutative affine algebraic group commonly found in projective algebraic geometry and toric geometry. Higher dimensional algebraic tori can be modelled as a product of algebraic groups . These groups were named by analogy with the theory of tori in Lie group theory (see Cartan subgroup). For example, over the complex numbers the algebraic torus is isomorphic to the group scheme , which is the scheme theoretic analogue of the Lie group . In fact, any -action on a complex vector space can be pulled back to a -action from the inclusion as real manifolds.
Tori are of fundamental importance in the theory of algebraic groups and Lie groups and in the study of the geometric objects associated to them such as symmetric spaces and buildings.
Algebraic tori over fields
In most places we suppose that the base field is perfect (for example finite or characteristic zero). This hypothesis is required to have a smooth group schemepg 64, since for an algebraic group to be smooth over characteristic , the maps must be geometrically reduced for large enough , meaning the image of the corresponding map on is smooth for large enough .
In general one has to use separable closures instead of algebraic closures.
Multiplicative group of a field
If is a field then the multiplicative group over is the algebraic group such that for any field extension the -points are isomor
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https://en.wikipedia.org/wiki/Electric%20field%20gradient
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In atomic, molecular, and solid-state physics, the electric field gradient (EFG) measures the rate of change of the electric field at an atomic nucleus generated by the electronic charge distribution and the other nuclei. The EFG couples with the nuclear electric quadrupole moment of quadrupolar nuclei (those with spin quantum number greater than one-half) to generate an effect which can be measured using several spectroscopic methods, such as nuclear magnetic resonance (NMR), microwave spectroscopy, electron paramagnetic resonance (EPR, ESR), nuclear quadrupole resonance (NQR), Mössbauer spectroscopy or perturbed angular correlation (PAC). The EFG is non-zero only if the charges surrounding the nucleus violate cubic symmetry and therefore generate an inhomogeneous electric field at the position of the nucleus.
EFGs are highly sensitive to the electronic density in the immediate vicinity of a nucleus. This is because the EFG operator scales as r−3, where r is the distance from a nucleus. This sensitivity has been used to study effects on charge distribution resulting from substitution, weak interactions, and charge transfer. Especially in crystals, the local structure can be investigated with above methods using the EFG's sensitivity to local changes, like defects or phase changes. In crystals the EFG is in the order of 1021V/m2. Density functional theory has become an important tool for methods of nuclear spectroscopy to calculate EFGs and provide a deeper understanding of
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https://en.wikipedia.org/wiki/Hybrid
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Hybrid may refer to:
Science
Hybrid (biology), an offspring resulting from cross-breeding
Hybrid grape, grape varieties produced by cross-breeding two Vitis species
Hybridity, the property of a hybrid plant which is a union of two different genetic parent strains
Hybrid (particle physics), a valence quark-antiquark pair and one or more gluons
Hybrid solar eclipse, a rare solar eclipse type
Technology
Transportation
Hybrid vehicle, a vehicle using more than one power source or an engine sourced from a different chassis
Hybrid electric vehicle, a vehicle using both internal combustion and electric power sources
Plug-in hybrid, whose battery can be recharged by a charging cable
Hybrid bicycle, a bicycle with features of road and mountain bikes
Hybrid train, a locomotive, railcar, or train that uses an onboard rechargeable energy storage system
Hybrid motorcycle, a motorcycle built using components from more than one original-manufacturer products, such as Norvin, TriBSA, or Triton
Hybrid rocket, a rocket motor using propellants from two different states of matter
Hybrid shipping container, a container using phase change material in combination with the ability to recharge itself
Electricity and electronics
Hybrid generator, an electric power system comprising two or more generators that supply power to a single output
Hybrid power, the combination of a power producer and the means to store that power in an energy storage medium
Hybrid power source, a stand-al
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